98-257 Griesemer M., Lutgen J.

Accumulation of Discrete Eigenvalues of the Radial Dirac Operator (41K, LaTeX 2e) 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 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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