 98257 Griesemer M., Lutgen J.
 Accumulation of Discrete Eigenvalues of the Radial Dirac Operator
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Apr 4, 98

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Abstract. For bounded potentials which behave like \(cx^{\gamma}\) at
infinity we investigate whether discrete eigenvalues of the radial
Dirac operator $H_{\kappa}$ accumulate at +1 or not. It is well
known that $\gamma=2$ is the critical exponent. We show that
\(c=1/8+\kappa(\kappa+1)/2\) is the critical coupling constant in
the case $\gamma=2$. Our approach is to transform the radial Dirac
equation into a SturmLiouville equation nonlinear in the spectral
parameter and to apply a new, general result on accumulation of
eigenvalues of such equations.
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