Bohr-Sommerfeld levels for quantum completely integrable systems. (English) Zbl 1483.81070
Summary: In this paper we will show how the Bohr-Sommerfeld levels of a quantum completely integrable system can be computed modulo \(O(\hbar^{\infty})\) by an inductive procedure starting at stage zero with the Bohr-Sommerfeld levels of the corresponding classical completely integrable system.
MSC:
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 58C40 | Spectral theory; eigenvalue problems on manifolds |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 81Q80 | Special quantum systems, such as solvable systems |
| 81V45 | Atomic physics |
References:
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