Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The strong convergence of Schrödinger propagators

Author: Alan D. Sloan
Journal: Trans. Amer. Math. Soc. 264 (1981), 557-570
MSC: Primary 47D05; Secondary 03H05, 35B99, 35J10, 81C05
MathSciNet review: 603781
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Abstract: Time dependent versions of the Trotter-Kato theorem are discussed using nonstandard analysis. Both standard and nonstandard results are obtained. In particular, it is shown that if a sequence of generators converges in the strong resolvent topology at each time to a limiting generator and if the sequence of generators and limiting generator uniformly satisfy Kisynski type hypotheses then the corresponding Schrodinger propagators converge strongly. The results are used to analyze time dependent, form bounded perturbations of the Laplacian.

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Keywords: Evolution equations, propagators, perturbations, Schrodinger equation
Article copyright: © Copyright 1981 American Mathematical Society