25. (a) The Hamiltonian for a system has the form H 1 = 1/2 ( 72²2 + P²³²₁^²) . Find the equation of motion for q. (b) Find a canonical transformation that reduces H to the form of a harmonic oscilla- tor. Show that the solution for the transformed variables is such that the equation of motion found in part (a) is satisfied.
25. (a) The Hamiltonian for a system has the form H 1 = 1/2 ( 72²2 + P²³²₁^²) . Find the equation of motion for q. (b) Find a canonical transformation that reduces H to the form of a harmonic oscilla- tor. Show that the solution for the transformed variables is such that the equation of motion found in part (a) is satisfied.
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Transcribed Image Text:25. (a) The Hamiltonian for a system has the form
1
1
= /²/ (√²/²2 + 1² 4²).
2
H
Find the equation of motion for q.
(b) Find a canonical transformation that reduces H to the form of a harmonic oscilla-
tor. Show that the solution for the transformed variables is such that the equation
of motion found in part (a) is satisfied.
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