The discrete and periodic heat and harmonic oscillator equation

DOI10.1080/10236190701427118zbMath1132.39013OpenAlexW2091119804MaRDI QIDQ5433503

Stefan Hilger

Publication date: 9 January 2008

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190701427118

zbMATH Keywords

heat equationtime scalesHeisenberg uncertainty relationSchrödinger harmonic oscillatorladder formalism

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Heat equation (35K05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Discrete version of topics in analysis (39A12) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (2)

Factorization of (q, h)-difference operators – an algebraic approach ⋮ The category of ladders

Cites Work

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• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Difference analogs of the harmonic oscillator
• Integrable systems on the lattice and orthogonal polynomials of discrete variable
• CANONICAL DISCRETIZATION I: DISCRETE FACES OF (AN)HARMONIC OSCILLATOR
• An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle
• The canonical Kravchuk basis for discrete quantum mechanics
• Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom

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