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On the Schrödinger equation with time-dependent electric fields

Published online by Cambridge University Press:  14 November 2011

Rafael José Iório Jr  and
Dan Marchesin
Rafael José Iório Jr
Affiliation:
Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, RJ, Brasil
Dan Marchesin
Affiliation:
Pontifícia Universidade Católica do Rio de Janeiro, RJ, Brasil, and Courant Institute of Mathematical Sciences, New York, U.S.A.
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Synopsis

We prove existence and uniqueness of solutions of i(∂ψ/∂t) = (−Δ+x1g(t)+q(x))ψ, ψ(x, s) = ψs (x) in ℝ3 for potentials q(x) including the Coulomb case. Existence and completeness of the wave operators is established for g(t) periodic with zero mean and q(x) short-range, smooth in the x1 direction. We characterize scattering and bound states in terms of the period operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 117 - 134
Copyright
Copyright © Royal Society of Edinburgh 1984

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