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Are wave functions uniquely determined by their position and momentum distributions?

Published online by Cambridge University Press:  17 February 2009

J. V. Corbett  and
C. A. Hurst
J. V. Corbett
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, N. S. W. 2113, Australia
C. A. Hurst
Affiliation:
Department of Mathematical Physics, University of Adelaide, Adelaide, South Australia 5001
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Abstract

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The problem of determining a square integrable function from both its modulus and the modulus of its Fourier transform is studied. It is shown that for a large class of real functions the function is uniquely determined from this data. We also construct fundamental subsets of functions that are not uniquely determined. In quantum mechanical language, bound states are uniquely determined by their position and momentum distributions but, in general, scattering states are not.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 2 , December 1977 , pp. 182 - 201
Copyright
Copyright © Australian Mathematical Society 1977

References

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