Spherically symmetric Dirac operators with variable mass and potentials infinite at infinity

Details Spherically symmetric Dirac operators with variable mass and potentials infinite at infinity Spherically symmetric Dirac operators with variable mass and potentials infinite at infinity

1998-04-20

arxiv.org/abs/math/9804091v1

Mathematics

Spectral Theory

16 pages; submitted to Publ. RIMS

Scientific paper

We study the spectrum of spherically symmetric Dirac operators in 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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