Gaussian Wave Packet for Time-dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p + p(1/x) Terms

Abstract

The exact solution of the Schrodinger equation is constructed for time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. The solution corresponds to a semiclassical Gaussian wave packet centered around the classical guiding trajectory. The behavior of the Gaussian wave packet we obtained is very similar to that of a classical wave packet because its guiding trajectory follows the classical equation of motion. Gaussian wave packets are ubiquitous in quantum mechanics and are fundamental states of many physical systems that exhibit various nonclassical properties.