1. Solution of the Cauchy problem for a time-dependent Schrödinger equation.
- Author
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Meiler, Maria, Cordero-Soto, Ricardo, and Suslov, Sergei K.
- Subjects
- *
PARTIAL differential equations , *CAUCHY problem , *HARMONIC oscillators , *DIFFERENTIAL operators , *INTEGRAL transforms , *BOUNDARY value problems , *INTEGRAL equations , *MATHEMATICAL physics - Abstract
We construct an explicit solution of the Cauchy initial value problem for the n-dimensional Schrödinger equation with certain time-dependent Hamiltonian operator of a modified oscillator. The dynamical SU(1,1) symmetry of the harmonic oscillator wave functions, Bargmann’s functions for the discrete positive series of the irreducible representations of this group, the Fourier integral of a weighted product of the Meixner–Pollaczek polynomials, a Hankel-type integral transform, and the hyperspherical harmonics are utilized in order to derive the corresponding Green function. It is then generalized to a case of the forced modified oscillator. The propagators for two models of the relativistic oscillator are also found. An expansion formula of a plane wave in terms of the hyperspherical harmonics and solution of certain infinite system of ordinary differential equations are derived as by-products. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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