The essential spectrum of Schrödinger operators with asymptotically constant magnetic fields on the Poincaré upper-half plane

Journal of Mathematical Physics

Volumn 44, Issue 1, 2003, Pages 89-106

  Inahama, Yuzuru ^a   Shirai, Shin Ichi ^b  

^a KYOTO UNIVERSITY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037251573     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1527717     Document Type: Article

References (23)

1. Antoine, M., Comtet, A., and Ouvry, S., "Scattering on a hyperbolic torus in a constant magnetic field," J. Phys. A 23, 3699-3710 (1990).
2. Avron, J. E. and Pnueli, A., "Landau Hamiltonians on symmetric spaces," in Ideas and Methods in Quantum and Statistical Physics, Vol. 2 (Cambridge University Press, Cambridge, 1992), pp. 96-111.
3. Benedict, M. G. and Molnár, B., "Algebraic construction of the coherent states of the Morse potential based on super-symmetric quantum mechanics," Phys. Rev. A 60, 1737-1740 (1999).
4. Birman, M. S. and Solomjak, M. Z., Spectral Theory of Self-adjoint Operators in Hüben Space (Reidel, Dordrecht, 1987).
5. Chernoff, P. R., "Note on product formulas for operator semigroups," J. Funct. Anal. 2, 238-242 (1968).
6. Comtet, A., "On the Landau levels on the hyperbolic space," Ann. Phys. 173, 185-209 (1987).
7. Cycon, H. L., Froese, R. G., Kirsch, W., and Simon, B., Schrödinger Operators (Springer-Verlag, New York, 1987).
8. Elstrodt, J., "Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, Teil I-III," Math. Ann. 203, 295-330 (1973);Math. Z. 132, 99-134 (1973); Math. Ann. 208, 99-132 (1974).
9. Elstrodt, J., "Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, Teil I-III," Math. Ann. 203, 295-330 (1973);Math. Z. 132, 99-134 (1973); Math. Ann. 208, 99-132 (1974).
10. Elstrodt, J., "Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, Teil I-III," Math. Ann. 203, 295-330 (1973);Math. Z. 132, 99-134 (1973); Math. Ann. 208, 99-132 (1974).
11. Fay, J., "Fourier coefficients of the resolvent for a Fuchsian group," J. Reine Angew. Math. 293, 143-203 (1977).
12. Grosche, C., "The path integral on the Poincaré upper half plane with a magnetic field and for the Morse potential," Ann. Phys. (N.Y.) 187, 110-134(1988).
13. Hörmander, L., An Introduction to Complex Analysis in Several Variables (Van Nostrand, Princeton, NJ, 1966).
14. Hörmander, L., Linear Partial Differential Operators (Springer-Verlag, Berlin, 1963).
15. Ikeda, N. and Matsumoto, H., "Brownian motion on the hyperbolic plane and Selberg trace formula," J. Funct. Anal. 163, 63-110 (1999).
16. Iwatsuka, A., "The essential spectrum of two-dimensional Schrödinger operators with perturbed constant magnetic fields," J. Math. Kyoto Univ. 23, 475-480 (1983).
17. Molnár, B., Benedict, M. G., and Bertrand, J., "Coherent states and the role of the affine group in the quantum mechanics of the Morse potential," J. Phys. A 34, 3139-3151 (2001).
18. Pitt, L. D., "A compactness condition for the Schrödinger operators on function spaces," J. Operator Theory 1, 49-54 (1979).
19. Roelcke, W., "Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I," Math. Ann. 167, 292-337 (1966).
20. Reed, M. and Simon, B., Methods of Modem Mathematical Physics, Vols. I-IV (Academic, New York, 1978).
21. Shigekawa, I., "Spectral properties of Schrödinger operators with magnetic fields for a spin 1/2 particle," J. Funct. Anal. 101, 255-285 (1991).
22. Shubin, M., "Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds," J. Funct. Anal. 186, 92-116 (2001).
23. Terras, A., Harmonic Analysis on Symmetric Spaces and Applications I (Springer-Verlag, Berlin, 1985).