The behavior of a quantum-mechanical harmonic oscillator under a random perturbation of the form f(t)q² is discussed. Equations are obtained governing the time evolution of the Wigner function and the weight function for the P representation. The latter function satisfies a fourth-order differential equation, in contrast to the simpler second-order equation obeyed by the Wigner function.
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B. R. Mollow (1970) studied this question.
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