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Spectral Properties of Schrödinger Operators with Irregular Magnetic Potentials, for a Spin 12 Particle

✍ Scribed by S.Z. Levendorskii

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
279 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

The two-dimensional Schrodinger operator H a for a spin particle is consid-¨2 ered. The magnetic field b generated by a does not grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum ˜Ž Ž .. Ž Ž .. Ä 4 H a consists of H a and 0 , the latter being an isolated eigenvalue of di sc infinite multiplicity, the former accumulating to qϱ only. The principal term of Ž Ž .. Ž Ž . . the asymptotics of H a , and of H a q V , where b and V do not grow di sc

in some directions, is computed.

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