| 1. | Define relations between the new generalized coordinates and the old canonical coordinates.
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| 2. | Define relations between the new generalized momenta and the old canonical coordinates.
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| 3. | Here is a canonical coordinate ( or ) and ( possibly ) the time.
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| 4. | The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers.
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| 5. | These are the metric canonical coordinates.
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| 6. | See canonical coordinates for more background.
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| 7. | Since the evolution of q depends upon four initial parameters, this means that there are four canonical coordinates.
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| 8. | A " canonical coordinate system " consists of canonical position and momentum variables that satisfy canonical Poisson-bracket relations,
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| 9. | Ideally, one can invert these relations to obtain formulae for each as a function of the old canonical coordinates.
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| 10. | The change of variable between one set of canonical coordinates and another is a "'canonical transformation " '.
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