We study the spectrum of spherically symmetric Dirac operators m three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the whole real line if the potential dominates the mass, or scalar potential, term. In the situation where the potential and the scalar potential are identical, the positive part of the spectrum is purely discrete: we show that the negative half-line is filled with purely absolutely continuous spectrum in this case.
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Karl Michael Schmidt, Osanobu Yamada, Spherically Symmetric Dirac Operators with Variable Mass and Potentials Infinite at Infinity. Publ. Res. Inst. Math. Sci. 34 (1998), no. 3, pp. 211–227DOI 10.2977/PRIMS/1195144693