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| Format: | Artículo científico |
| Language: | en |
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Sociedad Mexicana de Física A.C.
2009
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| Online Access: | https://www.redalyc.org/articulo.oa?id=57028304008 |
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Table of Contents:
- The Cauchy problem for a forced harmonic oscillator R.M. Lopez S.K. Suslov Física, Astronomía y Matemáticas Landau levels the Heisenberg Green functions Weyl group N (3) the Hermite polynomials We construct an explicit solution of the Cauchy initial value problem for the one-dimensional Schrodinger 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. 2009 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028304008 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.55