Semiclassical Asymptotics and Gaps in the Spectra of Magnetic Schrödinger Operators
- Cite this article as:
- Mathai, V. & Shubin, M. Geometriae Dedicata (2002) 91: 155. doi:10.1023/A:1016245930716
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In this paper, we study an L2 version of the semiclassical approximation of magnetic Schrödinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant μ goes to zero.