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The Hamiltonian for a 3-D isotropic harmonic oscillator is given by 1 •z [p² + p² +p² + µ² (q? + q² + q})]. Show that, F₁ H = = 92P3-93P2 and F₂ = μq₁ cos µt - p₁ sin ut are constants of motion.

The Hamiltonian for a 3-D isotropic harmonic oscillator is given by 1 •z [p² + p² +p² + µ² (q? + q² + q})]. Show that, F₁ H = = 92P3-93P2 and F₂ = μq₁ cos µt - p₁ sin ut are constants of motion.

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14.The Hamiltonian for a 3-D isotropic harmonic oscillator is given by 1 H [p? + p? + p를 + μ2 (q} + q글 + q})]. Show that, F, = q2P3 – 93P2 and F2 µq1 cos µt – P1 sin µt are constants of motion.
Transcribed Image Text:14.The Hamiltonian for a 3-D isotropic harmonic oscillator is given by 1 H [p? + p? + p를 + μ2 (q} + q글 + q})]. Show that, F, = q2P3 – 93P2 and F2 µq1 cos µt – P1 sin µt are constants of motion.
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