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Charlier Polynomials and Translational Invariance in the Quantum Harmonic Oscillator
Author(s) -
Szafraniec Franciszek Hugon
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200207)241:1<163::aid-mana163>3.0.co;2-w
Subject(s) - mathematics , creation and annihilation operators , operator (biology) , quantum harmonic oscillator , harmonic oscillator , quantum , ladder operator , property (philosophy) , polynomial , orthogonal polynomials , pure mathematics , mathematical physics , quantum mechanics , mathematical analysis , compact operator , physics , computer science , biochemistry , chemistry , philosophy , epistemology , repressor , transcription factor , extension (predicate logic) , gene , programming language
In a recent paper [5] the creation operator of the quantum harmonic oscillator (its counterpart, the annihilation one as well) is characterized through its (spatial) translational invariance property. Here we step up with replacing the operator theoretic reasoning of [5] by an orthogonal polynomial environment which let the arguments become natural. This settles the result well in the circumstances of [8] (as well as those of [7]).