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Integralproperties of hermite polynomials by operator methods

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Summary

The quantum mechanical method of the occupation number representation of the harmonic oscillator and the technique of noncommuting operators is used in the derivation of a master integral for Hermite polynomials. It contains not only nearly all integrals of this type given in the literature but gives more than twice this number new ones. The advantage in the derivation of the master integral is that it needs only elementary operator commutations.

Zusammenfassung

Die quantenmechanische Methode der Besetzungszahldarstellung des harmonischen Oszillators und Operatortechnik nichtvertauschbarer Operatoren werden zur Ableitung eines Grundintegrals mit Hermitischen Polynomen benutzt. Dieses enthält nicht nur fast alle in der Literatur bekannten Integrale mit Hermitischen Polynomen, sondern erlaubt auch die Aufstellung einer mehr als doppelt so grossen Zahl neuer Integrale. Der Vorteil bei der Ableitung des Grundintegrals ist, dass nur elementare Operatorvertauschungen nötig sind.

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Authors and Affiliations

  1. Institut für physikalische Chemie, TU Braunschweig, Germany

    Wolfgang Witschel

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  1. Wolfgang Witschel
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Witschel, W. Integralproperties of hermite polynomials by operator methods. Journal of Applied Mathematics and Physics (ZAMP) 24, 861–870 (1973). https://doi.org/10.1007/BF01590795

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  • DOI: https://doi.org/10.1007/BF01590795

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