Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-13T09:15:20.851Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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