HEM 2016: Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

hechoenmexico

Algunos colegas han sugerido incluir Math-Ph. Aquí empezamos (espero no omitir ningún preprint del 2016! Si conocen uno que no pongo, avisen por favor.)

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

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.

Comments: 17 pages, 3 tables
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:1601.05359 [math-ph]
(or arXiv:1601.05359v1 [math-ph] for this version)

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