The Cauchy Problem for a Forced Harmonic Oscillator
| dc.creator | Lopez, Raquel M. | |
| dc.creator | Suslov, Sergei K. | |
| dc.date | 2007-07-12 | |
| dc.date | 2007-12-27 | |
| dc.date.accessioned | 2026-07-07T08:51:02Z | |
| dc.date.available | 2026-07-07T08:51:02Z | |
| dc.description | 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. | |
| dc.description | 30 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0707.1902 | |
| dc.identifier | http://arxiv.org/abs/0707.1902 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144802 | |
| dc.subject | Mathematical Physics | |
| dc.title | The Cauchy Problem for a Forced Harmonic Oscillator | |
| dc.type | text |