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Basics
======

This program computes Clebsch-Gordon coefficients. Results are output in exact form (square roots
 of rational numbers) and in either an on-screen (human parseable, computer non-parseable) format,
 or in LaTeX code (computer parseable, human non-parseable.)


Usage
=====

View the bottom of the source file to input the particular coefficients desired. The syntax is 
 taken from Sakurai's 1994 (1985, 2011) textbook "Modern Quantum Mechanics." See page 211 to see
 it in action.

After editing the source for your desired decomposition (or just the specific coefficients 
 themselves), recompile like

    chmod 777 compile.sh
    ./compile.sh

 and then run the code like

    ./cgc

Be aware: the code may take a LONG time for certain values of parameters. "Why?" you ask?
 Since everything is done in exact form, a lay-mans version of symbolic computation is used for
 dealing with fractions and square roots of said fractions. If one were looking for floating
 point numbers, they could be generated, like, a cah-jillion times faster. This way was 
 preferrable when writing the code (before the speed was known.)


Motivation
==========

This program was written (from scratch, no cheating, no parents helping me glue glitter or
 anything) for the fourth assignment of Phys 500 - Quantum Mechanics at UBC in 2011.

Normally, I would not bother with Clebsch-Gordon coefficients, but I figured it would be fun
 to do something involving fractions. I also wanted to compute a large number of coefficients
 for future reference. Also - output directly into LaTeX format is handy for a number of 
 reasons.

Extra Info - Details
====================

One will not likely have a "\ket{  }" or "\braket{ }{ }" macro in LaTeX. If you decide you 
 want to use the LaTeX output, make sure to include the following macros in your source:

    \newcommand{\ket}[1]{\left| #1 \right>} % Use these rather than those garbage \rangle/mid/langle things.
    \newcommand{\bra}[1]{\left< #1 \right|} % These ones look much better because they can scale.
    \newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right|\left. #2 \vphantom{#1} \right>} % for Dirac brackets

 (or use the nearly equivalent "renewcommand" or "ensurecommand" or whatever.)


Additionally, if the output is not aligned to your perfection, make the
 following tweaks to the LaTeX output:

1 - Wrap the output with:
      \begin{empheq}{align}
          <output here>
      \end{empheq}
    (or simply the align environment, or whatever.)

2 - Change every '=' to a '&=' .

3 - Tack a '\\' onto every line except the last.

4 - Optionally add '\allowdisplaybreaks' and '\pagestyle{empty}' to the LaTeX header if your lines are 
    long or many.

 This is all pretty easy to do with some regular expressions: step 2 is s/=/\&=/   step 3 is s/$/\\\\/

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