\ProvidesPackage{physics}
% physics 1.3
% This material is subject to the LaTeX Project Public License.
% See http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html for the details of that license.
%
% Handy commands for physicists including macros for vectors, calculus, matrices, and bra-ket (Dirac) notation
% Requires xparse package, which comes bundled with l3packages and l3kernel
% This package loads amsmath, which comes standard with most latex distributions
% The commands defined in this package will silently overwrite previous commands with the same name, if such commands exist
%
% Created by Sergio C. de la Barrera
% Updated on December 12, 2012
% Uploaded on December 20, 2012
\RequirePackage{xparse}
\RequirePackage{amsmath}
% Options
\DeclareOption{trig}{\let\trigopt = 1}
\DeclareOption{notrig}{\let\trigopt = 0}
\DeclareOption{uprightdiff}{\def\diffd{\mathrm{d}}} % Upright differentials
\DeclareOption{italicdiff}{\def\diffd{d}} % Italic differentials
\DeclareOption{bolddel}{\DeclareDocumentCommand\vnabla{}{\boldsymbol\nabla}} % Vector bold \nabla symbol
\DeclareOption{arrowdel}{\DeclareDocumentCommand\vnabla{}{\vec{\boldsymbol\nabla}}} % Vector arrow \nabla symbol
\ExecuteOptions{trig,uprightdiff,bolddel}
\ProcessOptions\relax
% Symbols
\ProvideDocumentCommand\varE{}{\mathcal{E}} % Curly 'E'
\ProvideDocumentCommand\ordersymbol{}{\mathcal{O}} % Order symbol --> O(x^2)
\ProvideDocumentCommand\lparen{}{(} % Left parenthesis
\ProvideDocumentCommand\rparen{}{)} % Right parenthesis
% Brackets and braces
\DeclareDocumentCommand\quantity{}{{\ifnum\z@=`}\fi\@quantity}
\DeclareDocumentCommand\@quantity{ t\big t\Big t\bigg t\Bigg g o d() d|| }
{ % Flexible automatic bracketing of an expression in () or [] or {} or ||
% Handles manual override of sizing
\IfBooleanTF{#1}{\let\ltag\bigl \let\rtag\bigr}{
\IfBooleanTF{#2}{\let\ltag\Bigl \let\rtag\Bigr}{
\IfBooleanTF{#3}{\let\ltag\biggl \let\rtag\biggr}{
\IfBooleanTF{#4}
{\let\ltag\Biggl \let\rtag\Biggr}
{\let\ltag\left \let\rtag\right}
}
}
}
% Handles actual bracketing
\IfNoValueTF{#5}{
\IfNoValueTF{#6}{
\IfNoValueTF{#7}{
\IfNoValueTF{#8}
{()}
{\ltag\lvert{#8}\rtag\rvert}
}
{\ltag(#7\rtag) \IfNoValueTF{#8}{}{|#8|}}
}
{\ltag[#6\rtag] \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
}
{\ltag\lbrace#5\rtag\rbrace \IfNoValueTF{#6}{}{[#6]} \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
\ifnum\z@=`{\fi}
}
\DeclareDocumentCommand\qty{}{\quantity} % Shorthand for \quantity
\DeclareDocumentCommand\pqty{ l m }{\braces#1{\lparen}{\rparen}{#2}}
\DeclareDocumentCommand\bqty{ l m }{\braces#1{\lbrack}{\rbrack}{#2}}
\DeclareDocumentCommand\Bqty{ l m }{\braces#1{\lbrace}{\rbrace}{#2}}
\DeclareDocumentCommand\vqty{ l m }{\braces#1{\lvert}{\rvert}{#2}}
\DeclareDocumentCommand\pmqty{m}{\begin{pmatrix}#1\end{pmatrix}}
\DeclareDocumentCommand\Pmqty{m}{\left\lgroup\begin{matrix}#1\end{matrix}\right\rgroup}
\DeclareDocumentCommand\bmqty{m}{\begin{bmatrix}#1\end{bmatrix}}
\DeclareDocumentCommand\vmqty{m}{\begin{vmatrix}#1\end{vmatrix}}
\DeclareDocumentCommand\matrixquantity{}{{\ifnum\z@=`}\fi\@matrixquantity}
\DeclareDocumentCommand\@matrixquantity{ s g o d() d|| }
{
\mathord{
\IfNoValueTF{#2}
{
\IfNoValueTF{#3}
{
\IfNoValueTF{#4}
{
\IfNoValueTF{#5}
{()}
{\vmqty{#5}}
}
{
\IfBooleanTF{#1}
{\Pmqty{#4}}
{\pmqty{#4}}
\IfNoValueTF{#5}{}{|#5|}
}
}
{\bmqty{#3} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
}
{\begin{matrix}#2\end{matrix} \IfNoValueTF{#3}{}{[#3]} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
}
\ifnum\z@=`{\fi}
}
\DeclareDocumentCommand\mqty{}{\matrixquantity} % Shorthand for \matrixquantity
\DeclareDocumentCommand\matrixdeterminant{m}{\vmqty{#1}} % Matrix determinant
\DeclareDocumentCommand\mdet{}{\matrixdeterminant} % Shorthand for matrix determinant
\DeclareDocumentCommand\spmqty{m}{\pqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\sPmqty{m}{\left\lgroup\begin{smallmatrix}#1\end{smallmatrix}\right\rgroup}
\DeclareDocumentCommand\sbmqty{m}{\bqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\svmqty{m}{\vqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\smallmatrixquantity{ s g o d() d|| }
{
\mathord{
\IfNoValueTF{#2}
{
\IfNoValueTF{#3}
{
\IfNoValueTF{#4}
{
\IfNoValueTF{#5}
{()}
{\svmqty{#5}}
}
{
\IfBooleanTF{#1}
{\sPmqty{#4}}
{\spmqty{#4}}
\IfNoValueTF{#5}{}{|#5|}
}
}
{\sbmqty{#3} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
}
{\begin{smallmatrix}#2\end{smallmatrix} \IfNoValueTF{#3}{}{[#3]} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
}
}
\DeclareDocumentCommand\smqty{}{\smallmatrixquantity} % Shorthand for \smallmatrixquantity
\DeclareDocumentCommand\smallmatrixdeterminant{m}{\svmqty{#1}} % Small matrix determinant
\DeclareDocumentCommand\smdet{}{\smallmatrixdeterminant} % Shorthand for small matrix determinant
\DeclareDocumentCommand\argopen{s}{\IfBooleanTF{#1}{\mathopen{}\mathclose\bgroup}{\mathopen{}\mathclose\bgroup\left}} % Special open grouping for argument of a function
\DeclareDocumentCommand\argclose{s}{\IfBooleanTF{#1}{\egroup}{\aftergroup\egroup\right}} % Special close grouping for argument of a function
\DeclareDocumentCommand\braces{}{{\ifnum\z@=`}\fi\@braces}
\DeclareDocumentCommand\@braces{ s t\big t\Big t\bigg t\Bigg m m m }
{ % General braces with automatic and manual sizing
\IfBooleanTF{#1}
{\left#6\smash{#8}\right#7\vphantom{#8}}
{
\IfBooleanTF{#2}{\bigl#6{#8}\bigr#7}{
\IfBooleanTF{#3}{\Bigl#6{#8}\Bigr#7}{
\IfBooleanTF{#4}{\biggl#6{#8}\biggr#7}{
\IfBooleanTF{#5}{\Biggl#6{#8}\Biggr#7}{\left#6{#8}\right#7}
}
}
}
}
\ifnum\z@=`{\fi}
}
\DeclareDocumentCommand\fbraces{ s t\big t\Big t\bigg t\Bigg m m m m }
{ % Function braces with automatic and manual sizing
#8
\IfBooleanTF{#1}
{\argopen#6\smash{#9}\argclose#7\vphantom{#9}}
{
\IfBooleanTF{#2}{\argopen*\bigl#6{#9}\argclose*\bigr#7}{
\IfBooleanTF{#3}{\argopen*\Bigl#6{#9}\argclose*\Bigr#7}{
\IfBooleanTF{#4}{\argopen*\biggl#6{#9}\argclose*\biggr#7}{
\IfBooleanTF{#5}
{\argopen*\Biggl#6{#9}\argclose*\Biggr#7}
{\argopen#6{#9}\argclose#7}
}
}
}
}
}
\DeclareDocumentCommand\absolutevalue{ l m }{\braces#1{\lvert}{\rvert}{#2}} % Absolute value/complex modulus
\DeclareDocumentCommand\abs{}{\absolutevalue} % Shorthand for \absolutevalue
\DeclareDocumentCommand\norm{ l m }{\braces#1{\lVert}{\rVert}{#2}} % Norm
\DeclareDocumentCommand\order{ l m }{\fbraces#1{\lparen}{\rparen}{\ordersymbol}{#2}} % Order notation -> O(x^2)
\DeclareDocumentCommand\evaluated{ s g d[| d(| }
{ % Vertical evaluation bar
\IfNoValueTF{#2}
{
\IfNoValueTF{#3}
{
\IfNoValueTF{#4}
{\argopen.\vphantom{\int}\argclose\rvert}
{\IfBooleanTF{#1}{\vphantom{#4}}{}\left(\IfBooleanTF{#1}{\smash{#4}}{#4}\vphantom{\int}\right\rvert}
}
{\IfBooleanTF{#1}{\vphantom{#3}}{}\left[\IfBooleanTF{#1}{\smash{#3}}{#3}\vphantom{\int}\right\rvert \IfNoValueTF{#4}{}{(#4|}}
}
{\IfBooleanTF{#1}{\vphantom{#2}}{}\left.\IfBooleanTF{#1}{\smash{#2}}{#2}\vphantom{\int}\right\rvert \IfNoValueTF{#3}{}{[#3|} \IfNoValueTF{#4}{}{(#4|}}
}
\DeclareDocumentCommand\eval{}{\evaluated} % Shorthand for evaluated
\DeclareDocumentCommand\poissonbracket{ l m m }{\braces#1{\lbrace}{\rbrace}{#2,#3}} % Poisson bracket [same as anti-commutator]
\DeclareDocumentCommand\pb{}{\poissonbracket} % Shorthand for \poissonbracket
% Commutators
\DeclareDocumentCommand\commutator{ l m m }{\braces#1{\lbrack}{\rbrack}{#2,#3}} % Commutator
\DeclareDocumentCommand\comm{}{\commutator} % Shorthand for \commutator
\DeclareDocumentCommand\anticommutator{ l m m }{\braces#1{\lbrace}{\rbrace}{#2,#3}} % Anticommutator [same as Poisson bracket]
\DeclareDocumentCommand\acommutator{}{\anticommutator} % Shorthand for \anticommutator
\DeclareDocumentCommand\acomm{}{\anticommutator} % Shorthand for \anticommutator
% Vector notation
\DeclareDocumentCommand\vectorbold{ s m }{\IfBooleanTF{#1}{\boldsymbol{#2}}{\mathbf{#2}}} % Vector bold [star for Greek and italic Roman]
\DeclareDocumentCommand\vb{}{\vectorbold} % Shorthand for \vectorbold
\DeclareDocumentCommand\vectorarrow{ s m }{\IfBooleanTF{#1}{\vec{\boldsymbol{#2}}}{\vec{\mathbf{#2}}}} % Vector arrow + bold [star for Greek and italic Roman]
\DeclareDocumentCommand\va{}{\vectorarrow} % Shorthand for \vectorarrow
\DeclareDocumentCommand\vectorunit{ s m }{\IfBooleanTF{#1}{\boldsymbol{\hat{#2}}}{\mathbf{\hat{#2}}}} % Unit vector [star for Greek and italic Roman]
\DeclareDocumentCommand\vu{}{\vectorunit} % Shorthand for \vectorunit
\DeclareDocumentCommand\dotproduct{}{\boldsymbol\cdot} % Vector dot product symbol
\DeclareDocumentCommand\vdot{}{\dotproduct} % Shorthand for \dotproduct [note that the command sequence \dp is protected]
\DeclareDocumentCommand\crossproduct{}{\boldsymbol\times} % Vector cross product symbol
\DeclareDocumentCommand\cross{}{\crossproduct} % Shorthand for \crossproduct
\DeclareDocumentCommand\cp{}{\crossproduct} % Shorthand for \crossproduct
\DeclareDocumentCommand\gradient{ g o d() }{ % Gradient
\IfNoValueTF{#1}{
\IfNoValueTF{#2}{
\IfNoValueTF{#3}{\vnabla}{\fbraces{\lparen}{\rparen}{\vnabla}{#3}}
}
{\fbraces{\lbrack}{\rbrack}{\vnabla}{#2} \IfNoValueTF{#3}{}{(#3)}}
}
{\vnabla #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
}
\DeclareDocumentCommand\grad{}{\gradient} % Shorthand for \gradient
\DeclareDocumentCommand\divergence{ g o d() }{ % Divergence
\IfNoValueTF{#1}{
\IfNoValueTF{#2}{
\IfNoValueTF{#3}{\vnabla \vdot}{\vnabla \vdot \quantity(#3)}
}
{\vnabla \vdot \quantity[#2] \IfNoValueTF{#3}{}{(#3)}}
}
{\vnabla \vdot #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
}
\let\divisionsymbol\div % Rename \div [division symbol] in order to free up control sequence for \divergence
\let\div\relax
\DeclareDocumentCommand\div{}{\divergence} % Shorthand for \divergence
\DeclareDocumentCommand\curl{ g o d() }{ % Curl
\IfNoValueTF{#1}{
\IfNoValueTF{#2}{
\IfNoValueTF{#3}{\vnabla \cross}{\vnabla \cross \quantity(#3)}
}
{\vnabla \cross \quantity[#2] \IfNoValueTF{#3}{}{(#3)}}
}
{\vnabla \cross #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
}
\DeclareDocumentCommand\laplacian{ g o d() }{ % Laplacian
\IfNoValueTF{#1}{
\IfNoValueTF{#2}{
\IfNoValueTF{#3}{\nabla^2}{\fbraces{\lparen}{\rparen}{\nabla^2}{#3}}
}
{\fbraces{\lbrack}{\rbrack}{\nabla^2}{#2} \IfNoValueTF{#3}{}{(#3)}}
}
{\nabla^2 #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
}
% Operators
\DeclareMathOperator{\trace}{tr} % Trace of a matrix
\DeclareMathOperator{\Trace}{Tr} % Trace of a matrix (alternate)
\DeclareMathOperator{\rank}{rank} % Rank of a matrix
\DeclareMathOperator{\erf}{erf} % Gauss error function
\DeclareMathOperator{\Residue}{Res} % Residue
\DeclareDocumentCommand\principalvalue{g}{\IfNoValueTF{#1}{\mathcal{P}}{\mathcal{P}\mathord{#1}}}
\DeclareDocumentCommand\pv{}{\principalvalue}
\DeclareDocumentCommand\PV{g}{\IfNoValueTF{#1}{\mathrm{P.V.}}{\mathrm{P.V.}\mathord{#1}}}
\let\real\Re \DeclareDocumentCommand\Re{g}{\IfNoValueTF{#1}{\operatorname{Re}}{\fbraces{\lbrace}{\rbrace}{\operatorname{Re}}{#1}}}
\let\imaginary\Im \DeclareDocumentCommand\Im{g}{\IfNoValueTF{#1}{\operatorname{Im}}{\fbraces{\lbrace}{\rbrace}{\operatorname{Im}}{#1}}}
\DeclareDocumentCommand\opbraces{ m g o d() }
{
\IfNoValueTF{#2}
{
\IfNoValueTF{#3}
{
\IfNoValueTF{#4}
{#1}
{\fbraces{\lparen}{\rparen}{#1}{#4}}
}
{
\fbraces{\lbrack}{\rbrack}{#1}{#3}
\IfNoValueTF{#4}{}{(#4)}
}
}
{
\fbraces{\lbrace}{\rbrace}{#1}{#2}
\IfNoValueTF{#3}{}{[#3]}
\IfNoValueTF{#4}{}{(#4)}
}
}
\DeclareDocumentCommand\trigbraces{ m o d() }
{
\IfNoValueTF{#3}
{#1 \IfNoValueTF{#2}{}{[#2]}}
{#1 \IfNoValueTF{#2}{}{^{#2}} \argopen(#3\argclose)}
}
% Trig function and operator redefinitions
\ifx\trigopt 1
\let\sine\sin \DeclareDocumentCommand\sin{}{\trigbraces{\sine}}
\let\cosine\cos \DeclareDocumentCommand\cos{}{\trigbraces{\cosine}}
\let\tangent\tan \DeclareDocumentCommand\tan{}{\trigbraces{\tangent}}
\let\cosecant\csc \DeclareDocumentCommand\csc{}{\trigbraces{\cosecant}}
\let\secant\sec \DeclareDocumentCommand\sec{}{\trigbraces{\secant}}
\let\cotangent\cot \DeclareDocumentCommand\cot{}{\trigbraces{\cotangent}}
\let\arcsine\arcsin \DeclareDocumentCommand\arcsin{}{\trigbraces{\arcsine}}
\let\arccosine\arccos \DeclareDocumentCommand\arccos{}{\trigbraces{\arccosine}}
\let\arctangent\arctan \DeclareDocumentCommand\arctan{}{\trigbraces{\arctangent}}
\DeclareMathOperator{\arccosecant}{arccsc}
\DeclareDocumentCommand\arccsc{}{\trigbraces{\arccosecant}}
\DeclareMathOperator{\arcsecant}{arcsec}
\DeclareDocumentCommand\arcsec{}{\trigbraces{\arcsecant}}
\DeclareMathOperator{\arccotangent}{arccot}
\DeclareDocumentCommand\arccot{}{\trigbraces{\arccotangent}}
\DeclareMathOperator{\asine}{asin}
\DeclareDocumentCommand\asin{}{\trigbraces{\asine}}
\DeclareMathOperator{\acosine}{acos}
\DeclareDocumentCommand\acos{}{\trigbraces{\acosine}}
\DeclareMathOperator{\atangent}{atan}
\DeclareDocumentCommand\atan{}{\trigbraces{\atangent}}
\DeclareMathOperator{\acosecant}{acsc}
\DeclareDocumentCommand\acsc{}{\trigbraces{\acosecant}}
\DeclareMathOperator{\asecant}{asec}
\DeclareDocumentCommand\asec{}{\trigbraces{\asecant}}
\DeclareMathOperator{\acotangent}{acot}
\DeclareDocumentCommand\acot{}{\trigbraces{\acotangent}}
\let\hypsine\sinh \DeclareDocumentCommand\sinh{}{\trigbraces{\hypsine}}
\let\hypcosine\cosh \DeclareDocumentCommand\cosh{}{\trigbraces{\hypcosine}}
\let\hyptangent\tanh \DeclareDocumentCommand\tanh{}{\trigbraces{\hyptangent}}
\DeclareMathOperator{\hypcosecant}{csch}
\DeclareDocumentCommand\csch{}{\trigbraces{\hypcosecant}}
\DeclareMathOperator{\hypsecant}{sech}
\DeclareDocumentCommand\sech{}{\trigbraces{\hypsecant}}
\let\hypcotangent\coth \DeclareDocumentCommand\coth{}{\trigbraces{\hypcotangent}}
\let\exponential\exp \DeclareDocumentCommand\exp{}{\opbraces{\exponential}}
\let\logarithm\log \DeclareDocumentCommand\log{}{\trigbraces{\logarithm}}
\let\naturallogarithm\ln \DeclareDocumentCommand\ln{}{\trigbraces{\naturallogarithm}}
\let\determinant\det \DeclareDocumentCommand\det{}{\opbraces{\determinant}}
\let\Probability\Pr \DeclareDocumentCommand\Pr{}{\opbraces{\Probability}}
\DeclareDocumentCommand\tr{}{\opbraces{\trace}}
\DeclareDocumentCommand\Tr{}{\opbraces{\Trace}}
\DeclareDocumentCommand\Res{}{\opbraces{\Residue}}
\else
\DeclareMathOperator{\arccsc}{arccsc}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\arccot}{arccot}
\DeclareMathOperator{\asin}{asin}
\DeclareMathOperator{\acos}{acos}
\DeclareMathOperator{\atan}{atan}
\DeclareMathOperator{\acsc}{acsc}
\DeclareMathOperator{\asec}{asec}
\DeclareMathOperator{\acot}{acot}
\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\sech}{sech}
\DeclareDocumentCommand\tr{}{\trace}
\DeclareDocumentCommand\Tr{}{\Trace}
\DeclareDocumentCommand\Res{}{\Residue}
\fi
% Quick quad text (math-mode text with \quad spacing)
\DeclareDocumentCommand\qqtext{ s m }{\IfBooleanTF{#1}{}{\quad}\text{#2}\quad}
\DeclareDocumentCommand\qq{}{\qqtext}
\DeclareDocumentCommand\qcomma{}{,\quad}
\DeclareDocumentCommand\qc{}{\qcomma}
\DeclareDocumentCommand\qif{s}{\IfBooleanTF{#1}{}{\quad}\text{if}\quad}
\DeclareDocumentCommand\qthen{s}{\IfBooleanTF{#1}{}{\quad}\text{then}\quad}
\DeclareDocumentCommand\qelse{s}{\IfBooleanTF{#1}{}{\quad}\text{else}\quad}
\DeclareDocumentCommand\qotherwise{s}{\IfBooleanTF{#1}{}{\quad}\text{otherwise}\quad}
\DeclareDocumentCommand\qunless{s}{\IfBooleanTF{#1}{}{\quad}\text{unless}\quad}
\DeclareDocumentCommand\qgiven{s}{\IfBooleanTF{#1}{}{\quad}\text{given}\quad}
\DeclareDocumentCommand\qusing{s}{\IfBooleanTF{#1}{}{\quad}\text{using}\quad}
\DeclareDocumentCommand\qassume{s}{\IfBooleanTF{#1}{}{\quad}\text{assume}\quad}
\DeclareDocumentCommand\qsince{s}{\IfBooleanTF{#1}{}{\quad}\text{since}\quad}
\DeclareDocumentCommand\qlet{s}{\IfBooleanTF{#1}{}{\quad}\text{let}\quad}
\DeclareDocumentCommand\qfor{s}{\IfBooleanTF{#1}{}{\quad}\text{for}\quad}
\DeclareDocumentCommand\qall{s}{\IfBooleanTF{#1}{}{\quad}\text{all}\quad}
\DeclareDocumentCommand\qeven{s}{\IfBooleanTF{#1}{}{\quad}\text{even}\quad}
\DeclareDocumentCommand\qodd{s}{\IfBooleanTF{#1}{}{\quad}\text{odd}\quad}
\DeclareDocumentCommand\qinteger{s}{\IfBooleanTF{#1}{}{\quad}\text{integer}\quad}
\DeclareDocumentCommand\qand{s}{\IfBooleanTF{#1}{}{\quad}\text{and}\quad}
\DeclareDocumentCommand\qor{s}{\IfBooleanTF{#1}{}{\quad}\text{or}\quad}
\DeclareDocumentCommand\qas{s}{\IfBooleanTF{#1}{}{\quad}\text{as}\quad}
\DeclareDocumentCommand\qin{s}{\IfBooleanTF{#1}{}{\quad}\text{in}\quad}
\DeclareDocumentCommand\qcc{s}{\IfBooleanTF{#1}{}{\quad}\text{c.c.}\quad}
% Derivatives
\DeclareDocumentCommand\differential{ o g d() }{ % Differential 'd'
% o: optional n for nth differential
% g: optional argument for readability and to control spacing
% d: long-form as in d(cos x)
\IfNoValueTF{#2}{
\IfNoValueTF{#3}
{\diffd\IfNoValueTF{#1}{}{^{#1}}}
{\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}}
}
{\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}}
}
\DeclareDocumentCommand\dd{}{\differential} % Shorthand for \differential
\DeclareDocumentCommand\derivative{ s o m g d() }
{ % Total derivative
% s: star for \flatfrac flat derivative
% o: optional n for nth derivative
% m: mandatory (x in df/dx)
% g: optional (f in df/dx)
% d: long-form d/dx(...)
\IfBooleanTF{#1}
{\let\fractype\flatfrac}
{\let\fractype\frac}
\IfNoValueTF{#4}
{
\IfNoValueTF{#5}
{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}}}{\diffd #3\IfNoValueTF{#2}{}{^{#2}}}}
{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}}}{\diffd #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#5\argclose)}
}
{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}} #3}{\diffd #4\IfNoValueTF{#2}{}{^{#2}}}}
}
\DeclareDocumentCommand\dv{}{\derivative} % Shorthand for \derivative
\DeclareDocumentCommand\partialderivative{ s o m g g d() }
{ % Partial derivative
% s: star for \flatfrac flat derivative
% o: optional n for nth derivative
% m: mandatory (x in df/dx)
% g: optional (f in df/dx)
% g: optional (y in d^2f/dxdy)
% d: long-form d/dx(...)
\IfBooleanTF{#1}
{\let\fractype\flatfrac}
{\let\fractype\frac}
\IfNoValueTF{#4}
{
\IfNoValueTF{#6}
{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}}}
{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#6\argclose)}
}
{
\IfNoValueTF{#5}
{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}} #3}{\partial #4\IfNoValueTF{#2}{}{^{#2}}}}
{\fractype{\partial^2 #3}{\partial #4 \partial #5}}
}
}
\DeclareDocumentCommand\pderivative{}{\partialderivative} % Shorthand for \partialderivative
\DeclareDocumentCommand\pdv{}{\partialderivative} % Shorthand for \partialderivative
\DeclareDocumentCommand\variation{ o g d() }{ % Functional variation
% o: optional n for nth differential
% g: optional argument for readability and to control spacing
% d: long-form as in d(F(g))
\IfNoValueTF{#2}{
\IfNoValueTF{#3}
{\delta \IfNoValueTF{#1}{}{^{#1}}}
{\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}}
}
{\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}}
}
\DeclareDocumentCommand\var{}{\variation} % Shorthand for \variation
\DeclareDocumentCommand\functionalderivative{ s o m g d() }
{ % Functional derivative
% s: star for \flatfrac flat derivative
% o: optional n for nth derivative
% m: mandatory (g in dF/dg)
% g: optional (F in dF/dg)
% d: long-form d/dx(...)
\IfBooleanTF{#1}
{\let\fractype\flatfrac}
{\let\fractype\frac}
\IfNoValueTF{#4}
{
\IfNoValueTF{#5}
{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}}}{\variation #3\IfNoValueTF{#2}{}{^{#2}}}}
{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}}}{\variation #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#5\argclose)}
}
{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}} #3}{\variation #4\IfNoValueTF{#2}{}{^{#2}}}}
}
\DeclareDocumentCommand\fderivative{}{\functionalderivative} % Shorthand for \functionalderivative
\DeclareDocumentCommand\fdv{}{\functionalderivative} % Shorthand for \functionalderivative
% Bra-ket notation
\DeclareDocumentCommand\bra{ s m t\ket s g }
{ % Bra
\IfBooleanTF{#3}
{ % Contraction
\IfBooleanTF{#1}
{ % Bra has a star: no resize
\IfNoValueTF{#5}
{\braket*{#2}{} \IfBooleanTF{#4}{*}{}}
{\braket*{#2}{#5}}
}
{
\IfBooleanTF{#4}
{ % Ket has a star: no resize
\IfNoValueTF{#5}
{\braket{#2}{} *}
{\braket*{#2}{#5}}
}
{\braket{#2}{\IfNoValueTF{#5}{}{#5}}} % Neither term is starred: auto sizing
}
}
{ % No contraction
\IfBooleanTF{#1}
{\vphantom{#2}\left\langle\smash{#2}\right\rvert}
{\left\langle{#2}\right\rvert}
\IfBooleanTF{#4}{*}{}
\IfNoValueTF{#5}{}{#5}
}
}
\DeclareDocumentCommand\ket{ s m }
{ % Ket
\IfBooleanTF{#1}
{\vphantom{#2}\left\lvert\smash{#2}\right\rangle} % No resize
{\left\lvert{#2}\right\rangle} % Auto sizing
}
\DeclareDocumentCommand\innerproduct{ s m g }
{ % Inner product
\IfBooleanTF{#1}
{ % No resize
\IfNoValueTF{#3}
{\vphantom{#2}\left\langle\smash{#2}\middle\vert\smash{#2}\right\rangle}
{\vphantom{#2#3}\left\langle\smash{#2}\middle\vert\smash{#3}\right\rangle}
}
{ % Auto resize
\IfNoValueTF{#3}
{\left\langle{#2}\middle\vert{#2}\right\rangle}
{\left\langle{#2}\middle\vert{#3}\right\rangle}
}
}
\DeclareDocumentCommand\braket{}{\innerproduct} % Alternative for \innerproduct
\DeclareDocumentCommand\ip{}{\innerproduct} % Shorthand for \innerproduct
\DeclareDocumentCommand\outerproduct{ s m g }
{ % Dyad
\IfBooleanTF{#1}
{ % No resize
\IfNoValueTF{#3}
{\vphantom{#2}\left\lvert\smash{#2}\middle\rangle\!\middle\langle\smash{#2}\right\rvert}
{\vphantom{#2#3}\left\lvert\smash{#2}\middle\rangle\!\middle\langle\smash{#3}\right\rvert}
}
{ % Auto resize
\IfNoValueTF{#3}
{\left\lvert{#2}\middle\rangle\!\middle\langle{#2}\right\rvert}
{\left\lvert{#2}\middle\rangle\!\middle\langle{#3}\right\rvert}
}
}
\DeclareDocumentCommand\dyad{}{\outerproduct} % Alternative for \outerproduct
\DeclareDocumentCommand\op{}{\dyad} % Shorthand for \outerproduct
\DeclareDocumentCommand\ketbra{}{\dyad} % Alternative for \outerproduct
\DeclareDocumentCommand\expectationvalue{ s s m g }
{ % Expectation value
\IfNoValueTF{#4}
{
\IfBooleanTF{#1}
{\vphantom{#3}\left\langle\smash{#3}\right\rangle} % Starred implicit form: no resizing
{\left\langle{#3}\right\rangle} % Normal implicit form: auto sizing
}
{
\IfBooleanTF{#1}
{
\IfBooleanTF{#2}
{\left\langle{#4}\middle\vert{#3}\middle\vert{#4}\right\rangle} % Double starred explicit form: total auto sizing
{\vphantom{#3#4}\left\langle\smash{#4}\middle\vert\smash{#3}\middle\vert\smash{#4}\right\rangle} % Starred explicit form: no resizing
}
{\vphantom{#3}\left\langle{#4}\middle\vert\smash{#3}\middle\vert{#4}\right\rangle} % Normal explicit form: only resize based on bra/ket arguments
}
}
\DeclareDocumentCommand\expval{}{\expectationvalue} % Shorthand for \expectationvalue
\DeclareDocumentCommand\ev{}{\expectationvalue} % Shorthand for \expectationvalue
\DeclareDocumentCommand\vev{ m }{\expectationvalue{#1}{0}} % Vacuum expectation value
\DeclareDocumentCommand\matrixelement{ s s m m m }
{ % Matrix element
\IfBooleanTF{#1}
{
\IfBooleanTF{#2}
{\left\langle{#3}\middle\vert{#4}\middle\vert{#5}\right\rangle} % Double starred: total resizing
{\vphantom{#3#4#5}\left\langle\smash{#3}\middle\vert\smash{#4}\middle\vert\smash{#5}\right\rangle} % Starred: no resizing
}
{\vphantom{#4}\left\langle{#3}\middle\vert\smash{#4}\middle\vert{#5}\right\rangle} % Normal: only resize based on bra/ket arguments
}
\DeclareDocumentCommand\matrixel{}{\matrixelement} % Shorthand for \matrixelement
\DeclareDocumentCommand\mel{}{\matrixelement} % Shorthand for \matrixelement
% Matrix macros
\DeclareDocumentCommand\identitymatrix{m}
{
{
\newtoks\matrixtoks
\global\matrixtoks = {}
\newcount\rowcount
\newcount\colcount
\loop
\colcount = 0
\advance \rowcount by 1
{
\loop
\advance \colcount by 1
\edef\addtoks
{
\ifnum \colcount = 1 \else & \fi
\ifnum \colcount = \rowcount 1 \else 0 \fi
}
\global\matrixtoks = \expandafter{\the\expandafter\matrixtoks\addtoks}
\ifnum \colcount < #1
\repeat
}
\ifnum \rowcount < #1
\global\matrixtoks = \expandafter{\the\matrixtoks \\ }
\repeat
}
\the\matrixtoks
}
\DeclareDocumentCommand\imat{}{\identitymatrix}
\DeclareDocumentCommand\xmatrix{ s m m m }
{
{
\newtoks\matrixtoks
\global\matrixtoks = {}
\newcount\rowcount
\newcount\colcount
\loop
\colcount = 0
\advance \rowcount by 1
{
\loop
\advance \colcount by 1
\edef\addtoks{\ifnum \colcount = 1 \else & \fi #2 \IfBooleanTF{#1}{_{\ifnum #3 > 1 \the\rowcount \fi \ifnum #4 > 1 \the\colcount \fi}}{}}
\global\matrixtoks = \expandafter{\the\expandafter\matrixtoks\addtoks}
\ifnum \colcount < #4
\repeat
}
\ifnum \rowcount < #3
\global\matrixtoks = \expandafter{\the\matrixtoks \\ }
\repeat
}
\the\matrixtoks
}
\DeclareDocumentCommand\xmat{}{\xmatrix}
\DeclareDocumentCommand\zeromatrix{ m g }{\IfNoValueTF{#2}{\xmatrix{0}{#1}{#1}}{\xmatrix{0}{#1}{#2}}}
\DeclareDocumentCommand\zmat{}{\zeromatrix}
\DeclareDocumentCommand\paulixmatrix{}{0&1\\1&0}
\DeclareDocumentCommand\pauliymatrix{}{0&-i\\i&0}
\DeclareDocumentCommand\paulizmatrix{}{1&0\\0&-1}
\DeclareDocumentCommand\paulimatrix{m}
{
\let\argin=#1
\ifx\argin 0 \identitymatrix{2} \else
\ifx\argin 1 \paulixmatrix \else
\ifx\argin 2 \pauliymatrix \else
\ifx\argin 3 \paulizmatrix \else
\ifx\argin x \paulixmatrix \else
\ifx\argin y \pauliymatrix \else
\ifx\argin z \paulizmatrix \fi\fi\fi\fi\fi\fi\fi
}
\DeclareDocumentCommand\pmat{}{\paulimatrix}
\DeclareDocumentCommand\diagonalmatrix{O{} >{\SplitList{,}}m }{\@dmat{#1}#2}
\DeclareDocumentCommand\@dmat{mmggggggg}
{
\newtoks\matrixtoks
\global\matrixtoks = {}
\IfNoValueTF{#3}
{#2}
{
\IfNoValueTF{#4}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}}}
{
\IfNoValueTF{#5}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}}}
{
\IfNoValueTF{#6}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}}}
{
\IfNoValueTF{#7}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}}}
{
\IfNoValueTF{#8}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}}}
{
\IfNoValueTF{#9}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}}}
{\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}\\#1&\mqty{#9}}}
}
}
}
}
}
}
\the\matrixtoks
}
\DeclareDocumentCommand\dmat{}{\diagonalmatrix}
\DeclareDocumentCommand\antidiagonalmatrix{O{} >{\SplitList{,}}m }{\@admat{#1}#2}
\DeclareDocumentCommand\@admat{mmggggggg}
{
\newtoks\matrixtoks
\global\matrixtoks = {}
\IfNoValueTF{#3}
{#2}
{
\IfNoValueTF{#4}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\\mqty{#3}}}
{
\IfNoValueTF{#5}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\\mqty{#4}}}
{
\IfNoValueTF{#6}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\\mqty{#5}}}
{
\IfNoValueTF{#7}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\\mqty{#6}}}
{
\IfNoValueTF{#8}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\\mqty{#7}}}
{
\IfNoValueTF{#9}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\\mqty{#8}}}
{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}\\\mqty{#9}}}
}
}
}
}
}
}
\the\matrixtoks
}
\DeclareDocumentCommand\admat{}{\antidiagonalmatrix}
% Misc
\DeclareDocumentCommand\flatfrac{ m m }{\left.#1\middle\slash#2\right.}
\DeclareDocumentCommand\homework{}{ % You can try it
\ensuremath{
\div{\vb{E}}=\frac{\rho}{\epsilon_0} \qc
\div{\vb{B}}=0 \qc
\curl{\vb{E}}=-\pdv{\vb{B}}{t}\qc
\curl{\vb{B}}=\mu_0\vb{J}+\frac{1}{c^2}\pdv{\vb{E}}{t}\qc
H\ket{\Psi}=i\hbar\pdv{}{t}\ket{\Psi},
\qq{all else follows.}
}
}