On Forced Oscillations in Quantum Mechanics

H. Müller

Camille Lombard Latune, Bruno M. Escher, R. L. de Matos Filho +1 more

Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the unavoidable influence of noise. Here we obtain a quantum limit for the uncertainty in the estimation of the amplitude of a classical force with arbitrary time dependence, acting on a noisy quantum-mechanical oscillator. We determine the best initial state of the oscillator and the best measurement procedure, thus getting a rigorous and useful benchmark for experiments aiming to detect extremely small forces.

Jean Bellissard

Yukihisa Nogami

The accuracy of the adiabatic approximation in quantum mechanics is examined by applying it to the forced harmonic oscillator for which the time-dependent Schrödinger equation can be solved exactly. Nonadiabatic transitions caused by the external force that varies in time is focused on. A peculiar situation is illustrated such that, no matter how rapid and large the variation of the external force may be, all nonadiabatic transitions vanish exactly as t→∞.

Smith, T. B.

Using the Wigner-Weyl mapping of quantum mechanics to phase space we consider exactly the quantum mechanics of an harmonic oscillator driven by an external white noise force or whose frequency is time dependent, either adiabatically or parametrically. We find several transition probabilities exactly. We also consider the (quantum mechanical) randomizing effects of the external white noise force on the Weyl quantized phase angle and upon other Weyl quantized quantities.

Lazar Mayants