Consider the Hamiltonian of a 2D system to be H = (1/2m) (p^2x + p^2y) + (1/2)mω^2 (x^2 + y^2). Show that A = px^2 + m^2ω^2xy is a constant of motion.
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First, let's calculate the time derivative of A: dA/dt = d(px^2 + m^2ω^2xy)/dt Using the product rule, we can expand this derivative: dA/dt = d(px^2)/dt + d(m^2ω^2xy)/dt Now, let's calculate each term separately. Show more…
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