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Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators.
- Source :
-
Reviews in Mathematical Physics . May2024, p1. 23p. - Publication Year :
- 2024
-
Abstract
- We study the eigenvalue problem for a self-adjoint 1D Dirac operator. It is known that, near an energy level where the square of the potential makes a simple well, the eigenvalues are approximated by a Bohr–Sommerfeld type quantization rule. A remarkable difference from the Schrödinger case appears in the Maslov correction term. This fact was recently found by Hirota [Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov–Shabat operator, <italic>J. Math. Phys.</italic> <bold>58</bold> (2017) 102–108] under the analyticity condition of the potential using a complex WKB method. In this paper, we approach this problem with a microlocal technique focusing on the asymptotic behavior of the eigenfunction along the characteristic set to generalize the result to C∞ potentials. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0129055X
- Database :
- Academic Search Index
- Journal :
- Reviews in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 177206046
- Full Text :
- https://doi.org/10.1142/s0129055x24500247