On the invariance of the essential spectrum of an arbitrary operator. III
Published online by Cambridge University Press: 24 October 2008
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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