Spectral geometry: two exactly solvable models

作者: Yu.A. Kuperin , B.S. Pavlov , G.E. Rudin , S.I. Vinitsky

DOI: 10.1016/0375-9601(94)00725-5

关键词:

摘要: Abstract Two exactly solvable models illustrating the links between spectral properties of Hamiltonians, connections on induced Hilbert bundles and topological characteristics basis spaces are considered. The first them is based extension theory for symmetric operators second one-dimensional Laplace operator with parametrical boundary conditions.

参考文章(19)
Joseph Samuel, Rajendra Bhandari, General Setting for Berry's Phase Physical Review Letters. ,vol. 60, pp. 2339- 2342 ,(1988) , 10.1103/PHYSREVLETT.60.2339
J. M. Combes, P. Duclos, R. Seiler, Convergent expansions for tunneling Communications in Mathematical Physics. ,vol. 92, pp. 229- 245 ,(1983) , 10.1007/BF01210848
George A Hagedorn, Adiabatic expansions near eigenvalue crossings Annals of Physics. ,vol. 196, pp. 278- 295 ,(1989) , 10.1016/0003-4916(89)90179-6
Jan Segert, Non‐Abelian Berry’s phase, accidental degeneracy, and angular momentum Journal of Mathematical Physics. ,vol. 28, pp. 2102- 2114 ,(1987) , 10.1063/1.527422
A. Mostafazadeh, Arno R Bohm, Topological aspects of the non-adiabatic Berry phase Journal of Physics A. ,vol. 26, pp. 5473- 5480 ,(1993) , 10.1088/0305-4470/26/20/030
Frank Wilczek, A. Zee, Appearance of Gauge Structure in Simple Dynamical Systems Physical Review Letters. ,vol. 52, pp. 2111- 2114 ,(1984) , 10.1103/PHYSREVLETT.52.2111
B S Pavlov, The theory of extensions and explicitly-soluble models Russian Mathematical Surveys. ,vol. 42, pp. 127- 168 ,(1987) , 10.1070/RM1987V042N06ABEH001491
Toshihiro Iwai, A geometric setting for internal motions of the quantum three-body system Journal of Mathematical Physics. ,vol. 28, pp. 1315- 1326 ,(1987) , 10.1063/1.527534
Bernard Zygelman, Appearance of gauge potentials in atomic collision physics Physics Letters A. ,vol. 125, pp. 476- 481 ,(1987) , 10.1016/0375-9601(87)90189-7
Andrei A. Kvitsinsky, Seth Putterman, Adiabatic dynamics for a class of quantum Hamiltonians Letters in Mathematical Physics. ,vol. 21, pp. 133- 138 ,(1991) , 10.1007/BF00401647