Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem 53.1

Spin

Physics — Landau & Lifshitz · adiabatic-invariant-classical-oscillator

Problem

Determine the change in the adiabatic invariant for a classical oscillator which obeys the equation d2x/dt2+ω2(t)x=0,(1)\mathrm{d}^2x/\mathrm{d}t^2 + \omega^2(t)x = 0, \tag{1} when the frequency ω(t)\omega(t) varies slowly from its value ω1\omega_1 at t→−∞t \to -\infty to ω2\omega_2 at t→∞t \to \infty (A. M. Dykhne 1960).

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