# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/displaystyle{hbar^2over2m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle {\hbar^2\over 2m}$">|; 

$key = q/displaystyleleft.vphantom{{l(l+1)overr^2}+{2moverhbar^2}(V(r)-epsilon)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \left.\vphantom{ {l(l+1)\over r^2} +{2m\over\hbar^2}(V(r)-\epsilon)}\right)$">|; 

$key = q/displaystyleleft.vphantom{2c_2(2l+3)+left((2l+5)c_4+c_2^2right)r^2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle \left.\vphantom{ 2c_2(2l+3) +
\left((2l+5)c_4+c_2^2\right) r^2}\right)$">|; 

$key = q/displaystyle{R^2_{nlj}(r)+S^2_{nlj}(r)over4pir^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle {R^2_{nlj}(r)+S^2_{nlj}(r)\over 4\pi r^2}$">|; 

$key = q/displaystyleleft(vphantom{(l+1)r^le^{p(r)}+r^{l+1}e^{p(r)}p'(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle \left(\vphantom{(l+1)r^le^{p(r)} + r^{l+1}e^{p(r)}p'(r)}\right.$">|; 

$key = q/infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ \infty$">|; 

$key = q/left(vphantom{V(r_t)-epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$ \left(\vphantom{V(r_t)-\epsilon}\right.$">|; 

$key = q/Delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$ \Delta$">|; 

$key = q/displaystyleleft.vphantom{2{l+1overr}p'(r)+left[p(r)right]^2+p''(r)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \left.\vphantom{ 2{l+1\over r} p'(r)+\left[p(r)\right]^2+p''(r)
}\right)$">|; 

$key = q/displaystyleleft.vphantom{{doverdr}+{kappaoverr}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle \left.\vphantom{{d \over dr} + {\kappa\over r}}\right)$">|; 

$key = q/displaystyleleft[vphantom{p'(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \left[\vphantom{p'(r)}\right.$">|; 

$key = q/displaystyleleft.vphantom{p''(r_c)p''(r_c)}right]^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle \left.\vphantom{p''(r_c)p''(r_c)}\right]^{2}_{}$">|; 

$key = q/displaystyleleft(vphantom{2mc^2-V(r)+epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle \left(\vphantom{2mc^2 - V(r) + \epsilon }\right.$">|; 

$key = q/hbar;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$ \hbar$">|; 

$key = q/displaystyleleft.vphantom{V(r)-epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle \left.\vphantom{V(r)-\epsilon}\right)$">|; 

$key = q/displaystyleleft(vphantom{{doverdr}-{kappaoverr}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle \left(\vphantom{{d \over dr} - {\kappa\over r}}\right.$">|; 

$key = q/displaystyleDelta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle \Delta$">|; 

$key = q/scriptstylegamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\scriptstyle \gamma$">|; 

$key = q/displaystyle{AoverR_{nl}(r_t)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle {A\over R_{nl}(r_t)}$">|; 

$key = q/displaystyle{partialpsioverpartialr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle {\partial\psi\over\partial r}$">|; 

$key = q/displaystyle{dV(r)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle {dV(r)\over dr}$">|; 

$key = q/displaystyle{lsqrt{l^2-alpha^2Z^2}+(l+1)sqrt{(l+1)^2-alpha^2Z^2}over2l+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle {l\sqrt{l^2-\alpha^2 Z^2}+
(l+1)\sqrt{(l+1)^2-\alpha^2 Z^2}\over 2l+1}$">|; 

$key = q/displaystyle{kappaoverr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle {\kappa\over r}$">|; 

$key = q/displaystyleleft(vphantom{mbox{sin}theta{partialY_{lm}(hat{{bf{r})overpartialtheta}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \left(\vphantom{\mbox{sin}\theta{\partial Y_{lm}(\hat{\bf r})
\over\partial\theta}}\right.$">|; 

$key = q/displaystyle{partialY_{lm}(hat{{bf{r})overpartialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle {\partial Y_{lm}(\hat{\bf r})
\over\partial\theta}$">|; 

$key = q/displaystyleleft.vphantom{(2l+5)c_4+c_2^2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle \left.\vphantom{(2l+5)c_4+c_2^2}\right)$">|; 

$key = q/displaystylesqrt{{{l(l+1)overr^2}+left(V(r)-epsilonright)}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="74" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle \sqrt{{{l(l+1)\over r^2} + \left(V(r)-\epsilon\right)}}$">|; 

$key = q/displaystylesum_{{nlm}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \sum_{{nlm}}^{}$">|; 

$key = q/displaystyle{l(l+1)overr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle {l(l+1)\over r^2}$">|; 

$key = q/displaystyleint_{{r<r_c}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \int_{{r&lt;r_c}}^{}$">|; 

$key = q/displaystyleleft.vphantom{{1overmbox{sin}theta}{partialoverpartialtheta}left(mbo}^2theta}{partial^2Y_{lm}(hat{{bf{r})overpartialphi^2}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle \left.\vphantom{{1\over\mbox{sin}\theta}{\partial\over\partial\th...
...\mbox{sin}^2\theta}
{\partial^2Y_{lm}(\hat{\bf r})\over\partial\phi^2}
}\right)$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ \alpha$">|; 

$key = q/displaystylelangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle \langle$">|; 

$key = q/Theta_{{nl}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ \Theta_{{nl}}^{}$">|; 

$key = q/displaystyle{d^2f(x)overdx^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle {d^2 f(x)\over d x^2}$">|; 

$key = q/displaystyleleft.vphantom{-{hbar^2over2m}nabla^2+V(r)-epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \left.\vphantom{-{\hbar^2\over 2m}\nabla^2 + V(r)-\epsilon}\right)$">|; 

$key = q/displaystylerangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \rangle$">|; 

$key = q/displaystyleleft(vphantom{(2l+5)c_4+c_2^2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle \left(\vphantom{(2l+5)c_4+c_2^2}\right.$">|; 

$key = q/hat{{{bf{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$ \hat{{\bf r}}$">|; 

$key = q/displaystyle{1overR^{ps}(r)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle {1\over R^{ps}(r)}$">|; 

$key = q/displaystylesum_{{nlj}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \sum_{{nlj}}^{}$">|; 

$key = q/displaystylebf{r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle \bf r$">|; 

$key = q/displaystyle{dR_{nl}(r)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle {dR_{nl}(r)\over dr}$">|; 

$key = q/displaystyle{df(r)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle {d f(r)\over d r}$">|; 

$key = q/left.vphantom{V(r_t)-epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ \left.\vphantom{V(r_t)-\epsilon}\right)$">|; 

$key = q/displaystyle{dR(r_c)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle {dR(r_c)\over dr}$">|; 

$key = q/displaystyleTheta_{{nl}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle \Theta_{{nl}}^{}$">|; 

$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/displaystyleleft(vphantom{{l(l+1)overr^2}+M(r)left(V(r)-epsilonright)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle \left(\vphantom{ {l(l+1)\over r^2} + M(r)\left(V(r)-\epsilon\right)
}\right.$">|; 

$key = q/displaystyle{1overr^2mbox{sin}^2theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle {1\over r^2\mbox{sin}^2\theta}$">|; 

$key = q/displaystyleleft(vphantom{mbox{sin}theta{partialpsioverpartialtheta}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle \left(\vphantom{\mbox{sin}\theta{\partial\psi\over\partial\theta}}\right.$">|; 

$key = q/displaystyle{alpha^2over4M(r)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle {\alpha^2\over 4M(r)}$">|; 

$key = q/displaystyle{partial^2Y_{lm}(hat{{bf{r})overpartialphi^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle {\partial^2Y_{lm}(\hat{\bf r})\over\partial\phi^2}$">|; 

$key = q/displaystyleleft.vphantom{{1overr}{dR_{nl}(x)overdx}+langlekapparangle{R_{nl}(r)overr}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \left.\vphantom{{1\over r} {dR_{nl}(x)\over dx} +
\langle\kappa\rangle {R_{nl}(r)\over r}}\right)$">|; 

$key = q/displaystyleleft.vphantom{2{l+1overr}(2c_2r+4c_4r^3)+4c_2^2r^2+2c_2+12c_4r^2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle \left.\vphantom{ 2{l+1\over r} (2c_2r + 4c_4r^3)
+ 4c_2^2r^2 + 2c_2 + 12c_4r^2}\right)$">|; 

$key = q/displaystyleleft.vphantom{{l(l+1)overr^2}+M(r)left(V(r)-epsilonright)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle \left.\vphantom{ {l(l+1)\over r^2} + M(r)\left(V(r)-\epsilon\right)
}\right)$">|; 

$key = q/displaystyleleft(vphantom{V(r)-epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle \left(\vphantom{V(r)-\epsilon}\right.$">|; 

$key = q/displaystyle{d^nR(r_c)overdr^n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle {d^nR(r_c)\over dr^n}$">|; 

$key = q/displaystyleleft(vphantom{{1overr}{dR_{nl}(x)overdx}+langlekapparangle{R_{nl}(r)overr}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle \left(\vphantom{{1\over r} {dR_{nl}(x)\over dx} +
\langle\kappa\rangle {R_{nl}(r)\over r}}\right.$">|; 

$key = q/displaystyle{d^2R_{nl}(r)overdr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle {d^2 R_{nl}(r)\over dr^2}$">|; 

$key = q/displaystyle{d^2R_{nl}(x)overdx^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle {d^2 R_{nl}(x)\over d x^2}$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ \delta$">|; 

$key = q/displaystyleleft[vphantom{p''(r_c)p''(r_c)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \left[\vphantom{p''(r_c)p''(r_c)}\right.$">|; 

$key = q/displaystyleleft(vphantom{-{hbar^2over2m}{1overr}{d^2R_{nl}(r)overdr^2}+(V(r)-epsilon){1overr}R_{nl}(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \left(\vphantom{-{\hbar^2\over 2m} {1\over r} {d^2 R_{nl}(r)\over dr^2}
+(V(r)-\epsilon) {1\over r} R_{nl}(r)
}\right.$">|; 

$key = q/displaystylele;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \le$">|; 

$key = q/displaystyle{1overR^{ps}(r_c)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle {1\over R^{ps}(r_c)}$">|; 

$key = q/displaystyleTheta_{{nlj}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle \Theta_{{nlj}}^{}$">|; 

$key = q/displaystyleleft.vphantom{p'(r_c)}right]^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$\displaystyle \left.\vphantom{p'(r_c)}\right]^{2}_{}$">|; 

$key = q/displaystyle{1overr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle {1\over r}$">|; 

$key = q/displaystyleleft.vphantom{2mc^2-V(r)+epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\displaystyle \left.\vphantom{2mc^2 - V(r) + \epsilon }\right)$">|; 

$key = q/displaystyle{dR_{nl}(x)overdx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle {d R_{nl}(x)\over d x}$">|; 

$key = q/displaystyleleft(vphantom{{partialpsioverpartialr},{1overr}{partialpsioverpartiaheta},{1overrmbox{sin}theta}{partialpsioverpartialphi}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \left(\vphantom{{\partial\psi\over\partial r},
{1\over r}{\parti...
...theta},
{1\over r \mbox{sin}\theta}
{\partial\psi\over\partial\phi}
}\right.$">|; 

$key = q/displaystyle{l+1overr^3_c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle {l+1\over r^3_c}$">|; 

$key = q/ge;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$ \ge$">|; 

$key = q/displaystyle{l+1overr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle {l+1\over r}$">|; 

$key = q/displaystyleleft(vphantom{2{l+1overr}(2c_2r+4c_4r^3)+4c_2^2r^2+2c_2+12c_4r^2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle \left(\vphantom{ 2{l+1\over r} (2c_2r + 4c_4r^3)
+ 4c_2^2r^2 + 2c_2 + 12c_4r^2}\right.$">|; 

$key = q/displaystylegamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle \gamma$">|; 

$key = q/displaystyle{dR^{ps}(r)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle {dR^{ps}(r)\over dr}$">|; 

$key = q/langle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$ \langle$">|; 

$key = q/displaystyleleft.vphantom{p(r)}right]^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle \left.\vphantom{p(r)}\right]^{2}_{}$">|; 

$key = q/sim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ \sim$">|; 

$key = q/displaystyleleft.vphantom{(l+1)r^le^{p(r)}+r^{l+1}e^{p(r)}p'(r)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \left.\vphantom{(l+1)r^le^{p(r)} + r^{l+1}e^{p(r)}p'(r)}\right)$">|; 

$key = q/displaystylesum_{{nl}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \sum_{{nl}}^{}$">|; 

$key = q/le;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$ \le$">|; 

$key = q/displaystyle{partial^2psioverpartialphi^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle {\partial^2\psi\over\partial\phi^2}$">|; 

$key = q/displaystyle{d^nR^{ps}(r_c)overdr^n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle {d^nR^{ps}(r_c)\over dr^n}$">|; 

$key = q/rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$ \rangle$">|; 

$key = q/displaystyle{alpha^2over4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle {\alpha^2\over 4}$">|; 

$key = q/bullet;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$ \bullet$">|; 

$key = q/displaystyleleft.vphantom{mbox{sin}theta{partialY_{lm}(hat{{bf{r})overpartialtheta}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \left.\vphantom{\mbox{sin}\theta{\partial Y_{lm}(\hat{\bf r})
\over\partial\theta}}\right)$">|; 

$key = q/displaystyle{2(l+1)overr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle {2(l+1)\over r}$">|; 

$key = q/displaystylepsi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle \psi$">|; 

$key = q/displaystyleleft.vphantom{{hbar^2over2m}{l(l+1)overr^2}+V(r)-epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \left.\vphantom{ {\hbar^2\over 2m} {l(l+1)\over r^2} + V(r)-\epsilon
}\right)$">|; 

$key = q/displaystyle{doverdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle {d \over dr}$">|; 

$key = q/displaystylehat{{{bf{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle \hat{{\bf r}}$">|; 

$key = q/displaystyleleft[vphantom{p'(r_c)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle \left[\vphantom{p'(r_c)}\right.$">|; 

$key = q/thicksim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ \thicksim$">|; 

$key = q/displaystyle{partialoverpartialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle {\partial\over\partial\theta}$">|; 

$key = q/rho_{c}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ \rho_{c}^{}$">|; 

$key = q/displaystyleleft.vphantom{{doverdr}-{kappaoverr}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle \left.\vphantom{{d \over dr} - {\kappa\over r}}\right)$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ \theta$">|; 

$key = q/displaystyleleft.vphantom{{1overR^{ps}(r)}{d^2R^{ps}(r)overdr^2}-{l(l+1)overr^2}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle \left.\vphantom{{1\over R^{ps}(r)}{d^2R^{ps}(r)\over dr^2}
- {l(l+1)\over r^2}}\right)$">|; 

$key = q/displaystyleleft(vphantom{{1overmbox{sin}theta}{partialoverpartialtheta}left(mbo}^2theta}{partial^2Y_{lm}(hat{{bf{r})overpartialphi^2}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \left(\vphantom{{1\over\mbox{sin}\theta}{\partial\over\partial\th...
...\mbox{sin}^2\theta}
{\partial^2Y_{lm}(\hat{\bf r})\over\partial\phi^2}
}\right.$">|; 

$key = q/displaystylekappa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle \kappa$">|; 

$key = q/displaystyledelta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle \delta$">|; 

$key = q/displaystyle{dR_{nl}(r_t^+)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle {d R_{nl}(r_t^+)\over dr}$">|; 

$key = q/displaystyle{1overmbox{sin}^2theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle {1\over\mbox{sin}^2\theta}$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$ \epsilon$">|; 

$key = q/displaystyle{d^2f(r)overdr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle {d^2 f(r)\over d r^2}$">|; 

$key = q/displaystyleleft(vphantom{{hbar^2over2m}{l(l+1)overr^2}+V(r)-epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle \left(\vphantom{ {\hbar^2\over 2m} {l(l+1)\over r^2} + V(r)-\epsilon
}\right.$">|; 

$key = q/displaystyle{R_{nl}(r)overr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle {R_{nl}(r)\over r}$">|; 

$key = q/displaystyleleft(vphantom{{R_{nl}(r)overr}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle \left(\vphantom{{R_{nl}(r)\over r}}\right.$">|; 

$key = q/displaystyleleft(vphantom{2{l+1overr}p'(r)+left[p(r)right]^2+p''(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle \left(\vphantom{ 2{l+1\over r} p'(r)+\left[p(r)\right]^2+p''(r)
}\right.$">|; 

$key = q/displaystylege;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle \ge$">|; 

$key = q/displaystyle{d^2R^{ps}(r)overdr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle {d^2R^{ps}(r)\over dr^2}$">|; 

$key = q/displaystyle{d^2widetildeR_{nl}(r)overdr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle {d^2 \widetilde R_{nl}(r)\over dr^2}$">|; 

$key = q/displaystyleleft(vphantom{{1overR^{ps}(r)}{d^2R^{ps}(r)overdr^2}-{l(l+1)overr^2}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle \left(\vphantom{{1\over R^{ps}(r)}{d^2R^{ps}(r)\over dr^2}
- {l(l+1)\over r^2}}\right.$">|; 

$key = q/displaystyleleft.vphantom{mbox{sin}theta{partialpsioverpartialtheta}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \left.\vphantom{\mbox{sin}\theta{\partial\psi\over\partial\theta}}\right)$">|; 

$key = q/displaystyle{1overmbox{sin}theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle {1\over\mbox{sin}\theta}$">|; 

$key = q/displaystyle{1overrmbox{sin}theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle {1\over r \mbox{sin}\theta}$">|; 

$key = q/displaystyle{1overr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle {1\over r^2}$">|; 

$key = q/displaystylesimeq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle \simeq$">|; 

$key = q/displaystyle{dR_{nl}(r_t^-)overdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle {d R_{nl}(r_t^-)\over dr}$">|; 

$key = q/displaystyle{partialpsioverpartialphi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle {\partial\psi\over\partial\phi}$">|; 

$key = q/displaystyleleft|vphantom{{R_{nl}(r)overr}Y_{lm}(hatr)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle \left\vert\vphantom{{R_{nl}(r)\over r}Y_{lm}(\hat r)}\right.$">|; 

$key = q/displaystylehat{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle \hat{r}$">|; 

$key = q/displaystyleleft.vphantom{{l(l+1)overr^2}+{2(l+1)overr}p'(r)+left[p'(r)right]^2+p''(r)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle \left.\vphantom{ {l(l+1)\over r^2}+ {2(l+1)\over r}p'(r) +
\left[p'(r)\right]^2 + p''(r) }\right)$">|; 

$key = q/displaystyle{R^2_{nl}(r)over4pir^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle {R^2_{nl}(r)\over 4\pi r^2}$">|; 

$key = q/displaystyleint_{0}^{infty};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \int_{0}^{\infty}$">|; 

$key = q/displaystyle{d^2R^{ps}(r)overd^2r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle {d^2R^{ps}(r)\over d^2r}$">|; 

$key = q/displaystyle{partialpsioverpartialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle {\partial\psi\over\partial\theta}$">|; 

$key = q/rho_{v}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ \rho_{v}^{}$">|; 

$key = q/displaystyleleft(vphantom{-{hbar^2over2m}nabla^2+V(r)-epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\displaystyle \left(\vphantom{-{\hbar^2\over 2m}\nabla^2 + V(r)-\epsilon}\right.$">|; 

$key = q/displaystyleleft(vphantom{{l(l+1)overr^2}+{2(l+1)overr}p'(r)+left[p'(r)right]^2+p''(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle \left(\vphantom{ {l(l+1)\over r^2}+ {2(l+1)\over r}p'(r) +
\left[p'(r)\right]^2 + p''(r) }\right.$">|; 

$key = q/displaystyleleft(vphantom{{doverdr}+{kappaoverr}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle \left(\vphantom{{d \over dr} + {\kappa\over r}}\right.$">|; 

$key = q/displaystyleleft.vphantom{V(r)+epsilon}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle \left.\vphantom{ V(r) + \epsilon }\right)$">|; 

$key = q/rightarrow;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ \rightarrow$">|; 

$key = q/displaystyleleft(vphantom{V(r)+epsilon}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle \left(\vphantom{ V(r) + \epsilon }\right.$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ \rho$">|; 

$key = q/displaystyleleft(vphantom{{l(l+1)overr^2}+{2moverhbar^2}(V(r)-epsilon)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle \left(\vphantom{ {l(l+1)\over r^2} +{2m\over\hbar^2}(V(r)-\epsilon)}\right.$">|; 

$key = q/displaystyle{1overr^3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle {1\over r^3}$">|; 

$key = q/displaystyleleft.vphantom{{dR_{nl}(r)overdr}+langlekapparangle{R_{nl}(r)overr}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle \left.\vphantom{{dR_{nl}(r)\over dr} +
\langle\kappa\rangle {R_{nl}(r)\over r}}\right)$">|; 

$key = q/displaystylenabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \nabla$">|; 

$key = q/displaystyleepsilon_{{nl}}^{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \epsilon_{{nl}}^{}$">|; 

$key = q/displaystyle{df(x)overdx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle {d f(x)\over d x}$">|; 

$key = q/displaystyle{R(r_c)overr_c^{l+1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle {R(r_c)\over r_c^{l+1}}$">|; 

$key = q/displaystyleleft(vphantom{2c_2(2l+3)+left((2l+5)c_4+c_2^2right)r^2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \left(\vphantom{ 2c_2(2l+3) +
\left((2l+5)c_4+c_2^2\right) r^2}\right.$">|; 

$key = q/displaystyleleft(vphantom{{dR_{nl}(r)overdr}+langlekapparangle{R_{nl}(r)overr}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \left(\vphantom{{dR_{nl}(r)\over dr} +
\langle\kappa\rangle {R_{nl}(r)\over r}}\right.$">|; 

$key = q/displaystyle{l+1overr^2_c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle {l+1\over r^2_c}$">|; 

$key = q/displaystyleleft[vphantom{p(r)}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle \left[\vphantom{p(r)}\right.$">|; 

$key = q/displaystyleleft.vphantom{{R_{nl}(r)overr}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \left.\vphantom{{R_{nl}(r)\over r}}\right)$">|; 

$key = q/displaystyleepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle \epsilon$">|; 

$key = q/displaystyle{2moverhbar^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\displaystyle {2m\over\hbar^2}$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ \phi$">|; 

$key = q/displaystyleleft.vphantom{p'(r)}right]^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \left.\vphantom{p'(r)}\right]^{2}_{}$">|; 

$key = q/displaystylenabla^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle \nabla^{2}_{}$">|; 

$key = q/displaystyle{l+1overr_c};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle {l+1\over r_c}$">|; 

$key = q/displaystyleleft.vphantom{{R_{nl}(r)overr}Y_{lm}(hatr)}right|^{2}_{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \left.\vphantom{{R_{nl}(r)\over r}Y_{lm}(\hat r)}\right\vert^{2}_{}$">|; 

$key = q/displaystyleleft.vphantom{{partialpsioverpartialr},{1overr}{partialpsioverpartiaheta},{1overrmbox{sin}theta}{partialpsioverpartialphi}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle \left.\vphantom{{\partial\psi\over\partial r},
{1\over r}{\parti...
...theta},
{1\over r \mbox{sin}\theta}
{\partial\psi\over\partial\phi}
}\right)$">|; 

$key = q/displaystylene;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle \ne$">|; 

$key = q/displaystyle{partial^2overpartialr^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle {\partial^2\over\partial r^2}$">|; 

$key = q/displaystyle{1overr^2mbox{sin}theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle {1\over r^2\mbox{sin}\theta}$">|; 

$key = q/displaystyleleft.vphantom{-{hbar^2over2m}{1overr}{d^2R_{nl}(r)overdr^2}+(V(r)-epsilon){1overr}R_{nl}(r)}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \left.\vphantom{-{\hbar^2\over 2m} {1\over r} {d^2 R_{nl}(r)\over dr^2}
+(V(r)-\epsilon) {1\over r} R_{nl}(r)
}\right)$">|; 

$key = q/kappa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$ \kappa$">|; 

1;

