Complexified quantum rules. (English) Zbl 0909.58016

Lazutkin, V. F.; Terman, D. Ya.

Séminaire de théorie spectrale et géométrie. Année 1992-1993. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Math. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 11, 133-145 (1993).

Summary: The article gives a short account of papers published earlier in Russian. We formulate a generalization of well-known quantization rules by Bohr-Sommerfeld-Einstein-Keller-Maslov by adding terms which describe the tunneling of energy. This enables us to obtain imaginary radiational corrections to eigenvalues in the case of open systems as well as exponentially small splittings of eigenvalues in systems with symmetry.
For the entire collection see [Zbl 0812.00008].

MSC:

53D50	Geometric quantization
35P20	Asymptotic distributions of eigenvalues in context of PDEs
81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory

Keywords:

semiclassical approximation; eigenstates; Schrödinger equation; quantization; tunneling of energy