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On Hermite Functions, Integral Kernels, and Quantum Wires

Author

Listed:
  • Silvestro Fassari

    (Centro Europeo Ricerche in Fisica Matematica (CERFIM), P.O. Box 1132, CH-6601 Locarno, Switzerland
    Dipartimento di Scienze Ingegneristiche, Università degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy)

  • Manuel Gadella

    (Departamento de Física Teórica, Atómica y Óptica, and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Luis M. Nieto

    (Departamento de Física Teórica, Atómica y Óptica, and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Fabio Rinaldi

    (Centro Europeo Ricerche in Fisica Matematica (CERFIM), P.O. Box 1132, CH-6601 Locarno, Switzerland
    Dipartimento di Scienze Ingegneristiche, Università degli Studi Guglielmo Marconi, Via Plinio 44, I-00193 Rome, Italy)

Abstract

In this note, we first evaluate and subsequently achieve a rather accurate approximation of a scalar product, the calculation of which is essential in order to determine the ground state energy in a two-dimensional quantum model. This scalar product involves an integral operator defined in terms of the eigenfunctions of the harmonic oscillator, expressed in terms of the well-known Hermite polynomials, so that some rather sophisticated mathematical tools are required.

Suggested Citation

  • Silvestro Fassari & Manuel Gadella & Luis M. Nieto & Fabio Rinaldi, 2022. "On Hermite Functions, Integral Kernels, and Quantum Wires," Mathematics, MDPI, vol. 10(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3012-:d:893842
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    References listed on IDEAS

    as
    1. Enrico Celeghini & Manuel Gadella & Mariano A. del Olmo, 2022. "Symmetry Groups, Quantum Mechanics and Generalized Hermite Functions," Mathematics, MDPI, vol. 10(9), pages 1-21, April.
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