Principles of Quantum Mechanics · Problem 2.7.4

All Is Not Well with Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · canonical-transformations

Problem

Verify that the change to a rotated frame xˉ=xcos⁡θ−ysin⁡θ\bar{x} = x\cos\theta - y\sin\theta yˉ=xsin⁡θ+ycos⁡θ\bar{y} = x\sin\theta + y\cos\theta pˉx=pxcos⁡θ−pysin⁡θ\bar{p}_x = p_x\cos\theta - p_y\sin\theta pˉy=pxsin⁡θ+pycos⁡θ\bar{p}_y = p_x\sin\theta + p_y\cos\theta is a canonical transformation.

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