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Journal of Physics A Mathematical and General

Berry's phase and wavefunctions for time-dependent Hamilton systems

P. G. L. Leach

Published Jun 21, 1990• 28 citations
Publisher

Abstract

An alternative derivation of Berry's phase (1985) to that given by Morales (1988) is given for non-autonomous Hamiltonian systems which admit an energy-like first integral. The generality of the problems treated is greater.
DOI
10.1088/0305-4470/23/12/042

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We give a short review of some aspects of the dynamics of time-dependent quantum systems. In particular we discuss how to recast time-periodic quantum problems into an equivalent time-independent form, contrasting the results with those gained for a similar reformulation in the case of general time-dependence. This approach, usually known under the name of Floquet theory, can be used to clarify the structure of, for example, invariants of the given quantum system. We also apply it to the calculation of the Berry phase and show how it enables us to understand Berry phases for time-independent systems. This involves rewriting earlier work of the author in a coordinate-free fashion