%%% mathdefs.tex
%


% Taken from Adam Lupu-Sax ....................................................
%%% derivatives
\newcommand{\deriv}[2]{\frac{d#1}{d#2}}
\newcommand{\derivc}[3]{\left. \frac{d#1}{d#2}\right|_{#3}}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdc}[3]{\left. \frac{\partial #1}{\partial #2}\right|_{#3}}

%%% Dirac notation
\newcommand{\bra}[1]{\left\langle #1\right|}
\newcommand{\ket}[1]{\left|#1\right\rangle}
\newcommand{\braket}[2]{\left\langle #1 \left|#2\right.\right\rangle}
\newcommand{\braOket}[3]{\left\langle #1\left|#2\right|#3\right\rangle}

% calligraphic letters in math.
\def\cal#1{\mathcal{#1}}


% Taken from M Haggerty ......................................................
\def\avg#1{\left< #1 \right>}
\def\abs#1{\left| #1 \right|}
\def\recip#1{\frac{1}{#1}}
\def\vhat#1{\hat{{\bf #1}}}
\def\smallfrac#1#2{{\textstyle\frac{#1}{#2}}}
\def\smallrecip#1{\smallfrac{1}{#1}}

% SPSmith's definitions ......................................................
\def\spshalf{{1\over{2}}}
\def\Orabi{\Omega_{\rm rabi}}
\def\btt#1{{\tt$\backslash$#1}}




% My own .....................................................................

%%% Equations
\def\schrod{Schroedinger's Equation}
\def\helm{Helmholtz Equation}


%%% Equation environments
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\bean{\begin{mathletters}\begin{eqnarray}}
\def\eean{\end{eqnarray}\end{mathletters}}


%%% macros for Feb 2000 PRL
\newcommand{\tbox}[1]{\mbox{\tiny #1}}
\newcommand{\half}{\mbox{\small $\frac{1}{2}$}}
\newcommand{\pit}{\mbox{\small $\frac{\pi}{2}$}}
\newcommand{\sfrac}[1]{\mbox{\small $\frac{1}{#1}$}}
\newcommand{\mbf}[1]{{\mathbf #1}}
% hack to get APS's \text style to work ok:
\def\text{\tbox}

\newcommand{\mV}{{\mathsf{V}}}
\newcommand{\mL}{{\mathsf{L}}}
\newcommand{\mA}{{\mathsf{A}}}
\newcommand{\lB}{\lambda_{\tbox{B}}}  % de Broglie
\newcommand{\ofr}{{(\mbf{r})}}       % (r vec)
\def\ofkr{(k;\mbf{r})}			% (k;r vec)
\def\ofks{(k;\mbf{s})}			% (k;s vec)
\newcommand{\ofs}{{(\mbf{s})}}       % (s vec)
\def\xt{\mbf{x}^{\tbox T}}		% x^T vec

\def\ce{\tilde{C}_{\tbox E}}		% C_E
\def\cew{\tilde{C}_{\tbox E}(\omega)}		% C_E(w)
\def\ceqmw{\tilde{C}^{\tbox{qm}}_{\tbox E}(\omega)}	% C^qm_E(w)
\def\cewqm{\tilde{C}^{\tbox{qm}}_{\tbox E}}	% C^qm_E(w) no omega
\def\ceqm{C^{\tbox{qm}}_{\tbox E}}	% C^qm_E no tilde
\def\cw{\tilde{C}(\omega)}		% C(w)
\def\cfw{\tilde{C}_{\cal F}(\omega)}		% C_F(w)

\def\tcl{\tau_{\tbox{cl}}}		% tau cl
\def\tcol{\tau_{\tbox{col}}}		% tau col
\def\terg{t_{\tbox{erg}}}		% t_erg
\def\tbl{\tau_{\tbox{bl}}}		% tau bl
\def\theis{t_{\tbox{H}}}		% t_Heis

\def\area{\mathsf{A}_D}			% piston effective area A_D 
\def\ve{\nu_{\tbox{E}}}			% nu_E, noise intensity
\def\vewna{\nu_E^{\tbox{WNA}}}		% nu_E for WNA

\def\dxcqm{\delta x^{\tbox{qm}}_{\tbox c}}	% x to mix levels.

%% operators
\newcommand{\rop}{\hat{\mbf{r}}}	% vector valued operators
\newcommand{\pop}{\hat{\mbf{p}}}


%%% Integrals
\newcommand{\sint}{\oint \! d\mbf{s} \,} % surface int
\def\gint{\oint_\Gamma \!\! d\mbf{s} \,} % surface int over Gamma.
\newcommand{\lint}{\oint \! ds \,}	% d=2
\def\infint{\int_{-\infty}^{\infty} \!\!}	% infinite integral
\def\dn{\partial_n}				% d_n
\def\aswapb{a^*\!{\leftrightarrow}b}		% a* <-> b
\def\eps{\varepsilon}				% eps

%%% Dissipation.
\def\dhdxt{\partial {\cal H} / \partial x}
\def\dhdx{\pd{\cal H}{x}}
\def\dhdxnm{\left( \pd{\cal H}{x} \right)_{\!nm}}
\def\dhdxnmsq{\left| \left( \pd{\cal H}{x} \right)_{\!nm} \right| ^2}

%%% vergini
\def\bcs{\stackrel{\tbox{BCs}}{\longrightarrow}}	% apply BCs




%%% DIEL atom project.
\def\wx{\omega_x}
\def\wy{\omega_y}
\newcommand{\ofro}{({\bf r_0})}
\def\Eb{E_{\rm blue,rms}}
\def\Er{E_{\rm red,rms}}
\def\Es2{E_{0,{\rm sat}}^2}
\def\sb{s_{\rm blue}}
\def\sr{s_{\rm red}}

%%% text usefuls
\def\ie{{\it i.e.\ }}
\def\eg{{\it e.g.\ }}
\newcommand{\etal}{{\it et al.\ }}
\newcommand{\ibid}{{\it ibid.\ }}

%%% tables spaces.
\def\gap{\hspace{0.2in}}


%%%%%%%%%%%%%%%%%%%%
%%% mathletters code (from http://www.grad.uiuc.edu/thesis/latexcode.html )
% Modified Alex Barnett 00/9/28 to handle non-arabic \thechapter output
% (ie, now works in Appendices)
% Fails to give correct references in eqnarray (offset by one).
% Still inserts small extra space after equation - unknown reason.
%
%    Original code:
%\newcounter{eqletter}
%\def\mathletters{%
%\setcounter{eqletter}{0}%
%\addtocounter{equation}{1}
%\edef\curreqno{\arabic{equation}}
%\edef\@currentlabel{\theequation}
%\def\theequation{%
%\addtocounter{eqletter}{1}\arabic{chapter}.\curreqno\alph{eqletter}%
%}%
%}
%\def\endmathletters{\setcounter{equation}{\curreqno}}

\newcounter{eqletter}
\def\mathletters{%
\setcounter{eqletter}{0}%
\addtocounter{equation}{1}
\edef\curreqno{\arabic{equation}}
\edef\@currentlabel{\theequation}
\def\theequation{%
\addtocounter{eqletter}{1}\thechapter.\curreqno\alph{eqletter}%
}%
}
\def\endmathletters{\setcounter{equation}{\curreqno}}


%...............................................QPC...................

\newcommand{\bk}{{\bf k}}
\def\kf{k_{\text F}}
\newcommand{\br}{{\bf r}}
\newcommand{\TL}{{\text{(L)}}}
\newcommand{\TR}{{\text{(R)}}}
\newcommand{\TLR}{{\text{L,R}}}
\newcommand{\VSD}{V_{\text{SD}}}
\newcommand{\GT}{\Gamma_{\text{T}}}
\newcommand{\DEL}{\mbox{\boldmath $\nabla$}}
\def\lf{\lambda_{\text F}}
\def\st{\sigma_{\text T}}
\def\stlr{\sigma_{\text T}^{\text{L$\rightarrow$R}}}
\def\strl{\sigma_{\text T}^{\text{R$\rightarrow$L}}}
\def\aeff{a_{\text{eff}}}
\def\aaeff{A_{\text{eff}}}
\def\gat{G_{\text{atom}}}
\newcommand{\LB}{Landauer-B\"{u}ttiker}

% .............. NOTES ..................
% To force linebreak when get overfull hbox from equation in paragraph
% test, use \linebreak (which makes it justify the line it broke).
% Contrast \\ or \newline which leave empty space.
%
%