DESTRUCTION OF THE WAVE FUNCTION BY «WHITE» NOISE IN PARABOLIC POTENTIAL AT RESONANT DRIVE

Abstract

The quantum-mechanical problem of particle motion in a quadratic potential subject to dipole action periodically changing with time, and stochastic perturbation of the «white» noise type is considered. A similar situation is realized, in particular, when an electron moves along the crystal axis. A situation of this type is realized, in particular, when an electron moves along the crystal axis. In this case, the role of time in the problem is played by the depth of particle penetration, and the perturbation function describes forced oscillations of the crystal lattice. Another important example is associated with the calculation of the rate of a chemical reaction near localized anharmonic vibrations of atoms caused by thermal fluctuations or external influences. In this case, due to the large amplitude of localized anharmonic vibrations, the position of the potential well in which the particle is located can no longer be considered motionless, which requires a revision of the problem of calculating the wave function taking into account the dynamics of the potential well. The paper considers a parabolic potential, which as a whole is subject to a dipole effect periodically changing over time, as well as to the effect of stochastic «white» noise. Based on the found solutions to the non-stationary Schrödinger equation, algorithms for calculating the dynamics of the wave function are constructed. The evolution of the wave function of a particle is analyzed. Asymptotic solutions of the equation of motion are given, with the help of which the main characteristics of the wave packet are obtained. Examples of the evolution of the wave function are given for the selected type of perturbation of the potential. An example of the destruction (collapse) of the wave function due to the effect of noise is given. The effect of destruction (collapse) of the wave function, which occurs due to the impact of noise, is discovered. The influence of the amplitude of white noise on the characteristics of the collapse is studied. A hypothesis is proposed that the time before collapse is inversely proportional to the intensity of the noise.