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Are wave functions uniquely determined by their position and momentum distributions?
Published online by Cambridge University Press: 17 February 2009
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.
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- Copyright © Australian Mathematical Society 1977
References
REFERENCES
[1]Heliwig, G., Differential operators of mathematical physics (Addison-Wesley Pub. Co., Reading, Palo Alto, London, Don Mills, 1964), Ch. 6, Sect. 1.CrossRefGoogle Scholar
[2]Jauch, J. M., Foundations of quantum mechanics (Addison-Wesley Pub. Co., Reading, Menlo Park, London, Don Mills, 1968).Google Scholar
[4]Pauli, W., “Die aligemeinen Prinzipien der Wellenmechanik”, in Handbuch der Physik (Springer-Verlag, Berlin, 1958), Vol. 5, p. 17.Google Scholar
[5]Prugoveěki, E., Quantum mechanics in Hilbert space (Academic Press, New York and London, 1971).Google Scholar
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