The quantum relativistic harmonic oscillator: Spectrum of zeros of its wave functions

DOI10.1063/1.530105zbMath0787.33007OpenAlexW1965957636MaRDI QIDQ3136661

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Publication date: 21 October 1993

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

Full work available at URL: https://doi.org/10.1063/1.530105

zbMATH Keywords

WKB approximationquantum relativistic harmonic oscillatorrelativistic Hermite polynomialszeros of wave functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items

Asymptotics for the relativistic hermite polynomials zeros, Electrostatic models for zeros of polynomials: old, new, and some open problems, The moments of the density of zeros for the relativistic Hermite and Laguerre polynomials, The relativistic Hermite polynomial is a Gegenbauer polynomial, Algebraic and spectral properties of some quasiorthogonal polynomials encountered in quantum radiation, The relativistic szegö polynomials, Strong asymptotics for relativistic Hermite polynomials, A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces, Relativistic jacobi polynomials, Miscellaneous results on the generating functions of special functions, WKB approach to zero distribution of solutions of linear second order differential equations

Cites Work

• Spectral properties of the biconfluent Heun differential equation
• Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
• EQUILIBRIUM MEASURE AND THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS