%\usepackage{iso8859-1}
\usepackage{latexsym}
\textwidth 160mm
%\oddsidemargin 1mm
%\evensidema\ref{}rgin 1mm
%\marginparwidth 33mm 
%\marginparsep 3mmx
\textheight 234mm
\headsep 5mm
%%%\title{Forelesninger i kvantemekanikk\\ Bind I}
%%%\author{Ingjald Øverbø\\Fysisk Institutt,AVH}
%%%\date{Mai 1992}
%\includeonly{f}
\textwidth 165 mm

%\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\usepackage{isolatin1}
\usepackage[latin1]{inputenc}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%\maketitle
%\pagenumbering{roman}
%%\tableofcontents

%\pagenumbering{arabic}
%\renewcommand{\theequation}{\arabic{equation}}

%tatt inn fra bok.sty:
\newcommand{\fig}[1]{\mbox{Fig. \ref{#1}}}
% brukes slik: \fig{f15.1}

\newcommand{\tab}[1]{\mbox{tabell \ref{#1}}}
% brukes slik: \tab{t20.1}


\newcommand{\kap}[1]{\mbox{kap.\ \ref{#1}}}
% brukes slik: \kap{k3.1}

\newcommand{\kapeng}[1]{\mbox{Chap.\ \ref{#1}}}
% brukes slik: \kapeng{k3.1}

\newcommand{\avs}[1]{\mbox{avsn.\  \ref{#1}}}
% brukes slik: \avs{k4.1}

\newcommand{\avseng}[1]{\mbox{section  \ref{#1}}}
% brukes slik: \avseng{k4.1}

\newcommand{\be}[1]{\begin{equation}\label{#1}}
% brukes slik: ...\be{merkelapp}
\newcommand{\ee}{\end{equation}}

\newcommand{\BE}{\begin{equation}}

\newcommand{\Li}[1]{\mbox{lign.\ (\ref{#1})}}
% brukes slik: .. \Li{merkelapp} ,  gir lign. (1.2) 

\newcommand{\li}[1]{\mbox{(\ref{#1})}}
% brukes slik:  ..  \li{merkelapp},  gir (1.2) 

\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end  {eqnarray}}
% her må det settes inn en \label på slutten av hver linje som får et
% ligningsnummer.

\newcommand{\ba}{\begin{eqnarray*}}
% gir ligningssett uten nummer
\newcommand{\ea}{\end{eqnarray*}}

\newcommand{\barr}{\begin{array}}  % oblgat. arg. angir antall og posisjonering
\newcommand{\earr}{\end{array}}    % av kolonner, eks:{lcr}. Vertikal posisjon-
                                   % ering kan påvirkes med [t]{} eller [b]{},
                                   % om ønskelig.
                                   
\newcommand{\h}[1]{\hspace*{#1}}
\newcommand{\vv}[1]{\vspace*{#1}}
% brukes slik: \h{2mm}  \vv(-3mm}

\newcommand{\pde}{\partial}      % partiell derivert
\newcommand{\hs}{\hbar}          % h-strek
\newcommand{\rpil}{\rightarrow}       % høyrepil vanlig 
\newcommand{\lpil}{\leftarrow}       % venstrepil vanlig 
\newcommand{\Rpil}{\Rightarrow}       % høyrepil,dobbel
\newcommand{\lrpil}{\longrightarrow}      % høyrepil,vanlig lang
\newcommand{\lRpil}{\Longrightarrow}      % høyrepil,dobbel og lang 
\newcommand{\lLRpil}{\Longleftrightarrow} % venstrehøyrepil,dobbel og lang 
\newcommand{\opil}{\mbox{\boldmath$\uparrow$}}    % pil opp
\newcommand{\npil}{\mbox{\boldmath$\downarrow$}}  % pil ned
\newcommand{\prikk}{{\!\cdot\!}}   % brukes i skalarprodukter 
\newcommand{\Ast}{{\textstyle *}}
\newcommand{\Llc}[1]{\mbox{\large{#1}}} %Liten bokstav i 14 pt istd.f. 12 pt.
\newcommand{\dvs}{\h{3mm}\mbox{dvs.}\h{3mm}}
\newcommand{\osv}{\h{3mm}\mbox{osv.}}
\newcommand{\Exp}[1]{e^{\,\textstyle {#1}}}
\newcommand{\frli}[2]{{\textstyle\frac{#1}{#2}}} % liten brøk
\newcommand{\Hat}[1]{\hat{\Vec{#1}}} % enhetsvektor
\newcommand{\bma}[1]{\left(\barr{#1}} % starter matrise med f.eks. {cc}
\newcommand{\ema}{\earr\right)}       % avslutter samme matrise
\newcommand{\pfrac}[2]{\frac{\pde{#1}}{\pde{#2}}}
\newcommand{\hta}{\hspace*{3mm}} %  til bruk i tabell
% det som står ovenfor er tatt inn fra bok.sty





\newcommand{\hdx}{\frac{\hbar}{i} \frac{\partial}{\partial x}}  % h/i d/dx
\newcommand{\kinx}{-\frac{\hs^{2}}{2m} \frac{\pde^{2}}{\pde x^{2}}}
\newcommand{\Hamx}{\kinx+V(x)}
\newcommand{\Sch}{Schr\"od\-ing\-er\-lign\-ingen{}}
\newcommand{\Sche}{Schr\"odinger equation}
\newcommand{\Hamr}{\kinr+V(\Vec{r})}
\newcommand{\kinr}{-\frac{\hs^{2}}{2m}\nabv^2}
% \newcommand{\Vec}[1]{\mbox{\boldmath$\vec{#1}$}} % gir skrå vektorer
\newcommand{\MVec}[1]{\mbox{\boldmath${#1}$}} % til f.eks. nabla og andre greske
                                              % og matematiske?
\newcommand{\Vec}[1]{{\rm\bf{#1}}} % gir rett opp-stående vektorer
\newcommand{\prpr}[2]{\Vec{#1}\prikk\Vec{#2}} % prikkprodukt av vektorer
\newcommand{\krpr}[2]{\Vec{#1}\times\Vec{#2}} % kryssprodukt av vektorer
 \newcommand{\Psia}{\Psi^{\textstyle *}}
\newcommand{\psia}{\psi^{\textstyle *}}
\newcommand{\intuu}{\int_{-\infty}^{\infty}}
\newcommand{\intnu}{\int_{0}^{\infty}}
\newcommand{\FV}[1]{\LT\langle\,{#1}\,\RT\rangle} % forventningsverdi
\newcommand{\NN}{\nonumber}
\newcommand{\SLt}{i\hs\frac{\pde\Psi}{\pde t}=H\Psi}
\newcommand{\OG}[1]{\h{#1 mm}\mbox{og}\h{#1 mm}}
\newcommand{\OGE}[1]{\h{#1 mm}\mbox{and}\h{#1 mm}}
\newcommand{\IPR}{ i\Vec{p}\prikk\Vec{r}/\hs}
\newcommand{\IKR}{ i\Vec{k}\prikk\Vec{r}}
\newcommand{\IKRM}{ i\Vec{k}'\prikk\Vec{r}}
\newcommand{\IQR}{ i\Vec{Q}\prikk\Vec{r}}
\newcommand{\M}[1]{\hspace{2mm}${#1}$\hspace{2mm}}
\newcommand{\Schstx}{\frac{d^{2}\psi(x)}{dx^{2}}
                     =\frac{2m}{\hs^{2}}[V(x)-E]\psi(x)}
\newcommand{\ket}[1]{|\h{0.3mm}{#1}\h{0.3mm}\rangle}
\newcommand{\bra}[1]{\langle\h{0.3mm}{#1}\h{0.3mm}|}
\newcommand{\scpr}[2]{\langle\h{0.3mm}{#1}\h{0.3mm}|\h{0.3mm}{#2}\h{0.3mm}
\rangle}
\newcommand{\qed}{\h{3mm}\mbox{q.e.d.}}
\newcommand{\hdxm}{\frac{\hs}{i}\frac{\pde}{\pde x'}}  % \hs/i d/dx'
\newcommand{\enhetsmatrise}{1\h{-1.3mm}1}
\newcommand{\lag}{{\cal L}}
\newcommand{\nabv}{\MVec{\nabla}}
\newcommand{\DS}{\displaystyle}
\newcommand{\LT}{\left}
\newcommand{\RT}{\right}
\newcommand{\EF}{{\cal E}}
\newcommand{\EFV}{\MVec{\cal E}}
\newcommand{\mom}{{\cal M}}
\newcommand{\momv}{\MVec{\cal M}}
\newcommand{\RE}{\Re{\rm e}}
\newcommand{\IM}{\Im{\rm m}}
\newcommand{\CURL}[1]{\nabv\times\Vec{#1}}
\newcommand{\curl}[1]{\nabv\times\Vec{#1}}
\newcommand{\EPS}{\hat{\MVec{\varepsilon}}}
\newcommand{\EPSA}{\hat{\MVec{\varepsilon}}^{\Ast}}
\renewcommand{\dag}{\dagger}
\newcommand{\dagu}{^{\dag}}
\newcommand{\rk}{_{rk}}
\newcommand{\rkm}{_{r'k'}}
%\newcommand{\rk}{_{r\Vec{k}}}
%\newcommand{\kvec}{_\Vec{k}}
\newcommand{\kvec}{_k}
% må ha flere: Se side 269-270
\newcommand{\pkt}[1]{\paragraph{\underline{#1.}}}
\newcommand{\PKT}[1]{pkt.\ \underline{\Vec{#1}}}
\newcommand{\lamc}{\lambda\kern-0.5em\upper0.2ex{-}} %Prøve på $\lamc$.
\newcommand{\nno}{\newline\newline\noindent}
\newcommand{\spn}[2]{\bma{r}{#1}\\{#2}\ema}

\newcommand{\PV}{\Vec{p}}
\newcommand{\A}{\alpha}
\newcommand{\B}{\beta}
\newcommand{\SI}{\sigma}
\newcommand{\SIV}{\MVec{\sigma}}
\newcommand{\GA}{\gamma}
\newcommand{\la}{\lambda}
\newcommand{\LA}{\Lambda}
\newcommand{\GAM}{\gamma^{\mu}}
\newcommand{\GAN}{\gamma^{\nu}}
\newcommand{\GAV}{\MVec{\gamma}}
\newcommand{\PS}{\not\h{-0.8mm} p}   % p-slash
\newcommand{\AS}{\not\h{-0.4mm} a}   % a-slash
\newcommand{\LAS}{\not\h{-0.4mm} \la}   % lambda-slash, Compton-bølg.
\newcommand{\lsim}{\stackrel{<}{\sim}} %"mindre enn omtrent"
\newcommand{\gsim}{\stackrel{>}{\sim}} %"større enn omtrent"
\newcommand{\lapprox}{\stackrel{<}{\approx}} %"mindre enn eller tilnærmet lik"
\newcommand{\gapprox}{\stackrel{>}{\approx}} %"større enn eller tilnærmet lik"
\newcommand{\D}{\delta}
\newcommand{\dd}{\Delta}
\newcommand{\E}{\epsilon}
\newcommand{\om}{\omega}
\newcommand{\PD}{\Psi^{\dag}}
\newcommand{\AV}{\MVec{\alpha}}
\newcommand{\BV}{\MVec{\beta}}
\newcommand{\iqr}{\textstyle i\Vec{q}\prikk\Vec{r}}
\newcommand{\iQr}{\textstyle i\Vec{Q}\prikk\Vec{r}}
\newcommand{\HH}[1]{\hspace*{#1mm}}
\newcommand{\arccot}{\mbox{\,arccot\,}}
\newcommand{\hal}{\frli{1}{2}}
\newcommand{\alst}{\A^{\Ast}}
\newcommand{\ad}{a^{\dag}}
%\newcommand{\pkt}[1]{\paragraph{\underline{#1.}}}
%\newcommand{\PKT}[1]{pkt.\ \underline{\Vec{#1}}}
\newcommand{\ex}{\Hat{e}_x}
\newcommand{\ey}{\Hat{e}_y}
\newcommand{\ez}{\Hat{e}_z}
\newcommand{\ei}{\Hat{e}_i}
\newcommand{\ej}{\Hat{e}_j}
\newcommand{\er}{\Hat{e}_r}
\newcommand{\ephi}{\Hat{e}_{\phi}}
\newcommand{\eth}{\Hat{e}_{\theta}}
\newcommand{\ve}{\Vec}
\newcommand{\wtil}{\widetilde}
\newcommand{\prve}[1]{\dot{\ve{#1}}}
\newcommand{\pr}[1]{\dot{#1}}
\newcommand{\ver}{\ve{r}}
\newcommand{\vef}{\ve{F}}
\newcommand{\vep}{\ve{p}}
\newcommand{\vel}{\ve{L}}
\newcommand{\vev}{\ve{v}}
\newcommand{\veu}{\ve{u}}
\newcommand{\verp}{\ve{r}_{\perp}}
\newcommand{\rpp}{r_{\perp}}
\newcommand{\veom}{\MVec{\om}}
\newcommand{\ripp}{r_{i\perp}}
\newcommand{\verip}{\ver_{i\perp}}
\newcommand{\veg}{\ve{g}}
\newcommand{\vegeff}{\veg'_{\mbox{\small eff}}}
\newcommand{\vea}{\ve{a}}
\newcommand{\veaa}{\ve{A}}
\newcommand{\vefsent}{\vef_{\mbox{\small sentrifugal}}}
\newcommand{\vefcor}{\vef_{\mbox{\small Coriolis}}}
\newcommand{\vefeff}{\vef'_{\mbox{\small eff}}}
\newcommand{\ueff}{U_{\mbox{\small eff}}}
\newcommand{\feff}{F_{\mbox{\small eff}}}
\newcommand{\exd}{\dot{\Hat{e}}_x'}
\newcommand{\rmin}{r_{\mbox{\small min}}}
\newcommand{\eyd}{\dot{\Hat{e}}_y'}
\newcommand{\ezd}{\dot{\Hat{e}}_z'}
\newcommand{\exdd}{\ddot{\Hat{e}}_x'}
\newcommand{\eydd}{\ddot{\Hat{e}}_y'}
\newcommand{\ezdd}{\ddot{\Hat{e}}_z'}
\newcommand{\veomd}{\dot{\veom}}
\newcommand{\thd}{\dot{\theta}}
\newcommand{\thdd}{\ddot{\theta}}
\newcommand{\phid}{\dot{\phi}}
\newcommand{\verd}{\dot{\ver}}
\newcommand{\vepd}{\dot{\vep}}
\newcommand{\verdd}{\ddot{\ver}}
%\newcommand{\ddver2c}{\ddot{\ver}_{2c}}
\newcommand{\loe}{lø}
\newcommand{\si}{\sigma}
\newcommand{\siv}{\MVec{\si}}
\newcommand{\six}{\si_x}
\newcommand{\siy}{\si_y}
\newcommand{\siz}{\si_z}
\newcommand{\hatn}{\Hat{n}}
\newcommand{\hatx}{\Hat{x}}
\newcommand{\haty}{\Hat{y}}
\newcommand{\hatz}{\Hat{z}}
\newcommand{\hatp}{\Hat{p}}
\newcommand{\hatk}{\Hat{k}}
\newcommand{\hatr}{\Hat{r}}
\newcommand{\tyl}{\textstyle}
\renewcommand{\prikk}{{\bf\cdot}}
\newcommand{\iga}{_{\gamma}} 
\newcommand{\hatl}{\widehat{L}}
\newcommand{\hats}{\widehat{S}}
\newcommand{\hatj}{\widehat{J}}
\newcommand{\hhat}{\widehat{H}}
\newcommand{\hlve}{\widehat{\ve{L}}}
\newcommand{\hllve}{\widehat{\ve{L}}^2}
\newcommand{\hsve}{\widehat{\ve{S}}}
\newcommand{\hssve}{\widehat{\ve{S}}^2}
\newcommand{\hjve}{\widehat{\ve{J}}}
\newcommand{\hjjve}{\widehat{\ve{J}}^2}
\newcommand{\vemy}{\MVec{\mu}}
\newcommand{\vetau}{\MVec{\tau}}
\newcommand{\po}{\MVec{\uparrow}}
\newcommand{\pn}{\MVec{\downarrow}}
\newcommand{\boxeqa}[1]{\[\fbox{$\DS #1$}\]} % brukes slik: \boxeqa{ligning}
\newcommand{\boxeq}[2]{\be{#1}\fbox{${\DS #2}$}\ee} 
% brukes slik: \boxeq{ligningslabel}{ligning}
\newcommand{\bu}{$\spadesuit$}
\newcommand{\pop}{\widehat{p}}
\newcommand{\qop}{\widehat{q}}
\newcommand{\Fop}{\widehat{F}}
\newcommand{\Gop}{\widehat{G}}
\newcommand{\xop}{\widehat{x}}
\newcommand{\Kop}{\widehat{K}}
\newcommand{\vepop}{\widehat{\vep}}
\newcommand{\velop}{\widehat{\vel}}
\newcommand{\Aop}{\widehat{A}}
\newcommand{\Bop}{\widehat{B}}
\newcommand{\Dop}{\widehat{D}}
\newcommand{\Cop}{\widehat{C}}
%\newcommand{}{}
%\newcommand{}{}
%\newcommand{}{}
%\newcommand{}{}
%\newcommand{}{}

%\newcommand{}{}
%\include{f}
%\end{document}