The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials

DOI10.1063/1.1561156zbMath1062.39015arXivmath-ph/0207038OpenAlexW2079929399MaRDI QIDQ4832983

Matias Aunola

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/math-ph/0207038

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Discrete version of topics in analysis (39A12) Other special orthogonal polynomials and functions (33C47) Lamé, Mathieu, and spheroidal wave functions (33E10)

Related Items (2)

Computing elliptic membrane high frequencies by Mathieu and Galerkin methods ⋮ Real-time corrections to the effective potential

Uses Software

• MTIEU1

Cites Work

• Eigenvalues for infinite matrices
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
• The computation of eigenvalues and solutions of Mathieu's differential equation for noninteger order
• Precise determination of the energy levels of the anharmonic oscillator from the quantization of the angle variable
• Boundary-layer theory, strong-coupling series, and large-order behavior
• D-dimensional arrays of Josephson junctions, spin glasses and q-deformed harmonic oscillators
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
• Generalized \(q\)-Hermite polynomials

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