quantum-mechanics.tex

% Quantum Mechanics Flashcards
% Copyright 2007 Jason Underdown

\documentclass[avery5371,grid]{flashcards}

\usepackage[latin1]{inputenc}
\usepackage{amsfonts}
\usepackage{amsmath}

\cardfrontstyle[\large\slshape]{headings}
\cardbackstyle{empty}

\begin{document}
\cardfrontfoot{Quantum Mechanics}

\begin{flashcard}[Copyright \& License]{Copyright \copyright \, 2007 Jason Underdown \\
Some rights reserved.}
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These flashcards and the accompanying \LaTeX \, source code are licensed
under a Creative Commons Attribution--NonCommercial--ShareAlike 2.5 License.  
For more information, see creativecommons.org.  You can contact the author at:
\begin{center}
\begin{small}\tt jasonu [remove-this] at physics dot utah dot edu\end{small}
\end{center}
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\end{flashcard}

\begin{flashcard}[Equation]{Schr\"odinger equation\\non-operator form}
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\begin{displaymath}
i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m}
\frac{\partial^2 \Psi}{\partial x^2} + V \Psi
\end{displaymath}
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\end{flashcard}

\begin{flashcard}[Definition]{statistical interpretation of the wave function}
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\begin{displaymath}
\int_a^b |\Psi(x,t)|^2 dx =
\framebox[4.5cm]{\parbox[c]{4cm}{probability of finding the particle
between $a$ and $b$, at time $t$}}
\end{displaymath}
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\end{flashcard}

\begin{flashcard}[Formula]{Euler's formula}
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\begin{displaymath}
e^{i\theta} = \cos \theta + i\sin \theta
\end{displaymath}
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\end{flashcard}

\begin{flashcard}[Equation]{time--independent Schr\"odinger equation}
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The simplest way to write the time--independent Schr\"odinger equation is
$H\psi = E\psi$, however, with the Hamiltonian operator expanded it becomes:

\medskip
\begin{displaymath}
-\frac{\hbar^2}{2m} \frac{d^2 \psi}{dx^2} + V\psi = E\psi\\
\end{displaymath}
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\end{flashcard}

\begin{flashcard}[Definition]{Hamiltonian operator}
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\begin{displaymath}
\textrm{\^H} = -\frac{\hbar^2}{2m}\nabla^2 + V
\end{displaymath}
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\end{flashcard}

\end{document}