# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{}(J_zJ_+|lm;SPMgt;=(J_+J_z+hbarJ_+)|lm;SPMgt;=(m+1)hbarJ_+|lm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=381 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap175" SRC="img17.gif"  > '; 
$key = q/{}(J^2=frac12(J_+J_-+J_-J_+)+J^2_z){}/;
$cached_env_img{$key} = ' <IMG WIDTH=200 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap167" SRC="img9.gif"  > '; 
$key = q/{}(J_+J_-|j'm;SPMgt;Rightarrowl-j'^2+j'){}/;
$cached_env_img{$key} = ' <IMG WIDTH=186 HEIGHT=18 ALIGN=BOTTOM ALT="tex2html_wrap182" SRC="img24.gif"  > '; 
$key = q/{}(J_-=J_x-iJ_y=J^dagger_+){}/;
$cached_env_img{$key} = ' <IMG WIDTH=141 HEIGHT=22 ALIGN=BOTTOM ALT="tex2html_wrap163" SRC="img5.gif"  > '; 
$key = q/{}(RightarrowJ^2|lm;SPMgt;=lhbar^2|lm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=160 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap169" SRC="img11.gif"  > '; 
$key = q/{}(;SPMlt;p|J^2|p;SPMgt;=;SPMlt;p|overrightarrowJ^dagger*overrightarrowJ|p;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=200 HEIGHT=26 ALIGN=BOTTOM ALT="tex2html_wrap172" SRC="img14.gif"  > '; 
$key = q/{}(l,m){}/;
$cached_env_img{$key} = ' <IMG WIDTH=24 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap173" SRC="img15.gif"  > '; 
$key = q/{}(;SPMlt;lm|J^2-J^2_z|lm;SPMgt;=l-m^2=;SPMlt;lm|J_+J_+^dagger+J^dagger_+J_+|lm;SPMgt;Rightarrowlgeqm^2){}/;
$cached_env_img{$key} = ' <IMG WIDTH=476 HEIGHT=22 ALIGN=BOTTOM ALT="tex2html_wrap174" SRC="img16.gif"  > '; 
$key = q/{}(J_+=J_x+iJ_y){}/;
$cached_env_img{$key} = ' <IMG WIDTH=100 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap162" SRC="img4.gif"  > '; 
$key = q/{}([J_z,J_+]=hbarJ_+){}/;
$cached_env_img{$key} = ' <IMG WIDTH=101 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap164" SRC="img6.gif"  > '; 
$key = q/{}(J^2,J_z){}/;
$cached_env_img{$key} = ' <IMG WIDTH=39 HEIGHT=17 ALIGN=BOTTOM ALT="tex2html_wrap168" SRC="img10.gif"  > '; 
$key = q/{}(J^2J_pm|lm;SPMgt;=lhbar^2Jpm|lm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=190 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap177" SRC="img19.gif"  > '; 
$key = q/{}(;SPMlt;overrightarrowr|lm;SPMgt;=Y_lm(overrightarrowr)){}/;
$cached_env_img{$key} = ' <IMG WIDTH=146 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap188" SRC="img30.gif"  > '; 
$key = q/{}(existsj){}/;
$cached_env_img{$key} = ' <IMG WIDTH=14 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap179" SRC="img21.gif"  > '; 
$key = q/{}(j){}/;
$cached_env_img{$key} = ' <IMG WIDTH=6 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap184" SRC="img26.gif"  > '; 
$key = q/{}(RightarrowJ_pm|lm;SPMgt;=C_lmpmhbar^2|lmpm1;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=224 HEIGHT=19 ALIGN=BOTTOM ALT="tex2html_wrap178" SRC="img20.gif"  > '; 
$key = q/{}(l=0,34,2,154){}/;
$cached_env_img{$key} = ' <IMG WIDTH=121 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap186" SRC="img28.gif"  > '; 
$key = q/{}(J_zJ_-|lm;SPMgt;=(m-1)hbarJ_-|lm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=221 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap176" SRC="img18.gif"  > '; 
$key = q/{}(Y_lm){}/;
$cached_env_img{$key} = ' <IMG WIDTH=23 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap187" SRC="img29.gif"  > '; 
$key = q/{}(Rightarrowmin[-j,j]){}/;
$cached_env_img{$key} = ' <IMG WIDTH=99 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap183" SRC="img25.gif"  > '; 
$key = q/{}(Rightarrowj=0,12,1,32,...){}/;
$cached_env_img{$key} = ' <IMG WIDTH=159 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap185" SRC="img27.gif"  > '; 
$key = q/{}(J_+|lj;SPMgt;=0){}/;
$cached_env_img{$key} = ' <IMG WIDTH=78 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap180" SRC="img22.gif"  > '; 
$key = q/{}([overrightarrowa*overrightarrowJ,overrightarrowb*overrightarrowJ]=ihbar(overrightarrowaxoverrightarrowb)*overrightarrowJ){}/;
$cached_env_img{$key} = ' <IMG WIDTH=237 HEIGHT=23 ALIGN=BOTTOM ALT="tex2html_wrap161" SRC="img3.gif"  > '; 
$key = q/{}(J_z|lm;SPMgt;=mhbar|lm;SPMgt;){}/;
$cached_env_img{$key} = ' <IMG WIDTH=139 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap170" SRC="img12.gif"  > '; 
$key = q/{}([J_i,J_j]=ihbarepsilon_ijkJ_k){}/;
$cached_env_img{$key} = ' <IMG WIDTH=124 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap159" SRC="img1.gif"  > '; 
$key = q/{}(lgeq0){}/;
$cached_env_img{$key} = ' <IMG WIDTH=32 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap171" SRC="img13.gif"  > '; 
$key = q/{}([J_z,J_-]=-hbarJ_-){}/;
$cached_env_img{$key} = ' <IMG WIDTH=114 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap165" SRC="img7.gif"  > '; 
$key = q/{}([J^2,J_i]=0){}/;
$cached_env_img{$key} = ' <IMG WIDTH=76 HEIGHT=18 ALIGN=BOTTOM ALT="tex2html_wrap160" SRC="img2.gif"  > '; 
$key = q/{}([J_+,J_-]=2hbarJ_z){}/;
$cached_env_img{$key} = ' <IMG WIDTH=110 HEIGHT=16 ALIGN=BOTTOM ALT="tex2html_wrap166" SRC="img8.gif"  > '; 
$key = q/{}(J_-J_+|lj;SPMgt;Rightarrowl-j^2-j=0){}/;
$cached_env_img{$key} = ' <IMG WIDTH=193 HEIGHT=18 ALIGN=BOTTOM ALT="tex2html_wrap181" SRC="img23.gif"  > '; 

1;

