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VOL. 20 | 2019 Quasi-Classical Calculation of Eigenvalues by Maslov Quantization Condition
Tomoyo Kanazawa, Akira Yoshioka

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

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 Schr ödinger 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.

Information

Published: 1 January 2019
First available in Project Euclid: 21 December 2018

zbMATH: 1415.53063
MathSciNet: MR3887750

Digital Object Identifier: 10.7546/giq-20-2019-184-207

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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