Journal
MATHEMATICS
Volume 10, Issue 16, Pages -Publisher
MDPI
DOI: 10.3390/math10163012
Keywords
Gaussian potential; Birman-Schwinger operator; Hilbert-Schmidt operator; contact interaction
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Funding
- Spanish Ministerio de Ciencia e Innovacion (MCIN)
- European Union NextGenerationEU [PRTR C17.I1]
- Consejeria de Educacion, Junta de Castilla y Leon, through QCAYLE project by MCIN [PID2020-113406GB-I0]
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In this note, the authors evaluate and achieve an accurate approximation of a scalar product that plays a crucial role in determining the ground state energy in a two-dimensional quantum model. The calculation involves an integral operator defined in terms of the eigenfunctions of the harmonic oscillator expressed in Hermite polynomials, requiring sophisticated mathematical tools.
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.
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