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TURKISH JOURNAL OF PHYSICS

Extension of the class of exactly solvable nonstationary quantum mechanics problems

Aghayeva Rana Gazanfar

Published Jan 1, 2015• 0 citations
Publisher

Abstract

A modified factorization method for a charged particle in a time-dependent magnetic field has been developed by virtue of motion quantum integrals. Application of this method to the considered system helps to find exact solutions for a range of nonstationary potentials.
DOI
10.3906/fiz-1407-21

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Within the framework of Feynman path integration, expectation values of quantum mechanical operators may be exactly obtained for a class of time-dependent problems. Attention is focused on the two-dimensional motion of a charged particle in a perpendicular magnetic field with a time-dependent driving force. A harmonic oscillator potential is included to ensure that the corresponding density matrix is properly defined although some expectation values are defined without it. This potential is at least a mathematical convenience. Some discussion concerning the conditions under which steady states may be attained is also included.
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas unitary transformation approach is used when managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed to a much more simple system that is the sum of two independent harmonic oscillators which have time-dependent frequencies. We therefore easily identified the wave functions in the transformed system with the help of invariant operator of the system. The full wave functions in the original system is derived from the inverse unitary transformation of the wave functions associated to the transformed system.