- #1
darida
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Homework Statement
Show that
[itex]Q_{1}=\frac{1}{\sqrt{2}}(q_{1}+\frac{p_{2}}{mω})[/itex]
[itex]Q_{2}=\frac{1}{\sqrt{2}}(q_{1}-\frac{p_{2}}{mω})[/itex]
[itex]P_{1}=\frac{1}{\sqrt{2}}(p_{1}-mωq_{2})[/itex]
[itex]P_{2}=\frac{1}{\sqrt{2}}(p_{1}+mωq_{2})[/itex]
(where mω is a constant) is a canonical transformation by Poisson bracket test. This requires evaluating six simple Poisson brackets.
2. The attempt at a solution
[itex][Q_{1},P_{1}]=[\frac{∂Q_{1}}{∂q_{1}}\frac{∂P_{1}}{∂p_{1}}-\frac{∂Q_{1}}{∂p_{1}}\frac{∂P_{1}}{∂q_{1}}]+[\frac{∂Q_{1}}{∂q_{2}}\frac{∂P_{1}}{∂p_{2}}-\frac{∂Q_{1}}{∂p_{2}}\frac{∂P_{1}}{∂q_{2}}][/itex]
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etc
Correct?