Resonant Spread Wave Function in Parabolic Potential

Abstract

In this paper, we consider the parabolic potential, which as a whole is subject to dipole or quadrupole action (parametric resonance), which periodically changes with time, and the dynamics of the wave function of a particle. Based on the solutions found for the nonstationary 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, using which the main characteristics of the wave packet are obtained. For selected types of potential perturbations, examples of the evolution of the wave function are given.