On Hermite Functions, Integral Kernels, and Quantum Wires

On Hermite Functions, Integral Kernels, and Quantum Wires

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...

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Veröffentlicht in:Mathematics (Basel) 2022-08, Vol.10 (16), p.3012
Hauptverfasser: Fassari, Silvestro, Gadella, Manuel, Nieto, Luis M., Rinaldi, Fabio
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Approximation
Birman–Schwinger operator
contact interaction
Eigenvalues
Eigenvectors
Food science
Gaussian potential
Harmonic oscillators
Hermite polynomials
Hilbert–Schmidt operator
Investigations
Kernel functions
Mathematical analysis
Mathematical research
Operators (mathematics)
Quantum computing
Quantum physics
Quantum wires
Two dimensional models
Wire
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Beschreibung
Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10163012