Transient Effects for Continuously Observed Quantum Particle II

Abstract

The aim of this paper is to analyze the solution to the problem of the time-evolution of a Gaussian wave packet of quantum particle moving in the field of a linear force F(x) = ħγx with continuously observed position. Particular attention is paid to the case of a harmonic oscillator (γ < 0). In contrast to the case of unobserved particle for which the dispension of the packet oscillates, the oscillations for the observed particle are decaying and tend to a finite limit. It is shown that, like for a free quantum particle (γ = 0) [Open Syst. Information Dyn. 5, 391 (1998), Phys. Rev. A 60, 687 (1999)], the position dispersion function (for all γ, negative or positive) always decreases in the beginning of the observation. Next, the dispersion function oscillates, at first irregularly, and passing through a regular rapidly decaying oscillations achieves its asymptotic value. The same is true for the case of a coherent state for which the position dispersion for the unobserved particle is constant. It is also shown that for the initial coherent state the asymptotic position dispersion is always smaller than the initial one.