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Quasi-classical calculation of eigenvalues by Maslov quantization condition. (English) Zbl 1415.53063

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 20th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 2–7, 2018. Sofia: Avangard Prima; Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 20, 184-207 (2019).
Summary: The Maslov quantization condition is a condition for Lagrangian submanifolds which is regarded as a mathematical extension of the Bohr-Sommerfeld quantization condition. In this survey note, we apply the Maslov quantization condition to several concrete Schrödinger operators and quantize invariant Lagrangian submanifolds of their classical systems. We see the quasi-classical energy levels are equal to the quantum ones for these operators and also the number of Lagrangian submanifolds is equal to the multiplicities of eigenvalues for these operators.
For the entire collection see [Zbl 1408.53003].

MSC:

53D12 Lagrangian submanifolds; Maslov index
81S10 Geometry and quantization, symplectic methods
53D50 Geometric quantization
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