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On the invariance of the essential spectrum of an arbitrary operator. III

Published online by Cambridge University Press:  24 October 2008

Martin Schechter
Martin Schechter
Affiliation:
Belfer Graduate School of Science, Yeshiva University
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Extract

The spectrum of the hydrogen energy operator

(Δ is the Laplacian and r is the distance from the origin) consists of the non-negative real axis and a sequence of negative eigenvalues of finite multiplicities converging to O. In the present study we are interested in finding sufficient conditions on a potential q(x) such that the spectrum of the operator

in En has a ‘hydrogen-like’ spectrum, i.e. a spectrum consisting of

(a) the non-negative real axis,

(b) at most a denumerable set of negative eigenvalues of finite multiplicities having zero as its only possible limit point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 975 - 984
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

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