Year: 2007
Type: preprint
Abstract: We construct an explicit solution of the Cauchy initial value problem for the one-dimensional Schroedinger equation with a time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg-Weyl group N(3) in a certain special case first, and then is extended to the general case. A three parameter extension of the classical Fourier integral is discussed as a by-product. Motion of a particle with a spin in uniform perpendicular magnetic and electric fields is considered as an application; a transition amplitude between Landau levels is evaluated in terms of Charlier polynomials. In addition, we also solve an initial value problem to a similar diffusion-type equation.
Source: arXiv (Cornell University)
Authors: Lopez, Raquel M., Suslov, Sergei K.
Institution: Arizona State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2108501029