Geodesic
Classical and quantum integrability of Hamiltonians without scattering states
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 249-268

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We establish that every quantum Hamiltonian without scattering states has a complete family of conserved quantities independently of the dimension of the system. This result leads to a comparison of the general properties of classical and quantum integrable systems. We discuss several relevant examples and an application to the statistical distribution of energies. As a spin-off, we obtain additional support for the Berry–Tabor conjecture without taking the semiclassical limit into account.
Keywords: quantum mechanics, integrability, spectral theory, Berry–Tabor conjecture. 
@article{TMF_2006_148_2_a6,
     author = {A. Enciso and D. Peralta-Salas},
     title = {Classical and quantum integrability of {Hamiltonians} without scattering states},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {249--268},
     publisher = {mathdoc},
     volume = {148},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a6/}
}
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A. Enciso; D. Peralta-Salas. Classical and quantum integrability of Hamiltonians without scattering states. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 249-268. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a6/