Principles of Quantum Mechanics · Problem 2.8.4

All Is Not Well with Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · symmetries-generator-phase-space

Problem

Consider H=12p2+12x2\mathscr{H} = \frac{1}{2}p^2 + \frac{1}{2}x^2, which is invariant under infinitesimal rotations in *phase space* (the xx-pp plane). Find the generator of this transformation (after verifying that it is canonical). (You could have guessed the answer based on Exercise 2.5.2.).

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