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Accumulation of Discrete Eigenvalues of the Radial Dirac Operator

✍ Scribed by Marcel Griesemer; Joseph Lutgen

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 148 KB
Volume: 162
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3360

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✦ Synopsis

For bounded potentials which behave like &cx &# at infinity we investigate whether discrete eigenvalues of the radial Dirac operator H } accumulate at +1 or not. It is well known that #=2 is the critical exponent. We show that c=1Â8+ }(}+1)Â2 is the critical coupling constant in the case #=2. Our approach is to transform the radial Dirac equation into a Sturm Liouville equation nonlinear in the spectral parameter and to apply a new, general result on accumulation of eigenvalues of such equations.

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