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A class of time periodic Hamiltonians with no bound states

Published online by Cambridge University Press:  14 November 2011

H. Kaneta
H. Kaneta
Affiliation:
Department of Mathematics, Faculty of Science, Okayama University, Okayama 700, Japan
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Synopsis

We generalise the Paley–Wiener closedness theorem and apply it to a class of time periodic Hamiltonians to show that all solutions to the corresponding Schrodinger equation decay.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 37 - 42
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Coddington, E. A. and Levinson, N.. Theory of ordinary differential equations (New York: McGraw-Hill, 1955).Google Scholar
2Hartman, P.. Ordinary differential equations (New York: John Wiley & Sons, 1972).Google Scholar
3Howland, J. S.. Scattering theory for Hamiltonians periodic in time. Indiana Univ. Math. J. 28 (1979), 471–494.CrossRefGoogle Scholar
4Kato, T.. Integration of the equation of evolution in a Banach space. J. Math. Soc. Japan. 5 (1953), 209–234.CrossRefGoogle Scholar
5Kato, T.. Perturbation theory for linear operators, 2nd edn. (Berlin: Springer, 1976).Google Scholar
6Kitada, H. and Yajima, K.. A scattering theory for time-dependent long range potentials. Duke Math. J. 49 (1982), 341–376.CrossRefGoogle Scholar
7Paley, R. E. A. C. and Wiener, N.. Fourier transform in the complex domain (Providence, R.I.: Amer. Math. Soc, 1934).Google Scholar
8Reed, M. and Simon, B.. Method of modern mathematical physics, Vol. IV (New York and London:Academic Press, 1978).Google Scholar
9Yajima, K. and Kitada, H.. Bound states and scattering states for time periodic Hamiltonians. Ann. Inst. H. Poincari Sect A, 34 (1983), 145–157.Google Scholar