The semiclassical small-ℏ limit of loci of roots of subdominant solutions for polynomial potentials

DOI10.1063/1.3598419zbMath1317.81124arXiv0805.0373OpenAlexW2076762453MaRDI QIDQ5266058

Stefan Giller

Publication date: 29 July 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.0373

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)

Related Items (1)

Bender-Wu singularities

Cites Work

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• Complex zeros of real ergodic eigenfunctions
• Zeros of eigenfunctions of some anharmonic oscillators
• High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials
• WKB approach to zero distribution of solutions of linear second order differential equations
• Conjecture on the interlacing of zeros in complex Sturm–Liouville problems
• Borel summable solutions to one-dimensional Schrödinger equation
• Complex Zeros of Eigenfunctions of 1D Schrodinger Operators
• The high energy semiclassical asymptotics of loci of roots of fundamental solutions for polynomial potentials
• Exactness of conventional and supersymmetric JWKB formulae and their relation to the shape invariance property of potentials

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