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International Journal of Theoretical Physics

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

J. R. Choi, In Hyun Nahm

Published Nov 27, 2006• 23 citations
Publisher
DOI
10.1007/s10773-006-9050-2

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We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.