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Abstract: We construct an explicit solution of the Cauchy initial value problem for theone-dimensional Schroedinger equation with a time-dependent Hamiltonianoperator for the forced harmonic oscillator. The corresponding Green functionpropagator is derived with the help of the generalized Fourier transform anda relation with representations of the Heisenberg-Weyl group N3 in a certainspecial case first, and then is extended to the general case. A three parameterextension of the classical Fourier integral is discussed as a by-product.Motion of a particle with a spin in uniform perpendicular magnetic and electricfields is considered as an application; a transition amplitude between Landaulevels is evaluated in terms of Charlier polynomials. In addition, we alsosolve an initial value problem to a similar diffusion-type equation.

Autor: Raquel M. Lopez, Sergei K. Suslov


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