Geodesic
Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential
Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 6, pp. 608-615
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By taking advantage of Wang’s results on the scalar product of four eigenfunctions of the 1D harmonic oscillator, we explicitly calculate the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by a Gaussian potential, showing that it can be written as a ratio of Gamma functions.
Keywords: Gaussian potential, Birman-Schwinger operator, trace class operator, harmonic oscillator. 
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     author = {S. Fassari and F. Rinaldi},
     title = {Exact calculation of the trace of the {Birman{\textendash}Schwinger} operator of the one-dimensional harmonic oscillator perturbed by an attractive {Gaussian} potential},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {608--615},
     year = {2019},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2019_10_6_a0/}
}
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S. Fassari; F. Rinaldi. Exact calculation of the trace of the Birman–Schwinger operator of the one-dimensional harmonic oscillator perturbed by an attractive Gaussian potential. Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 6, pp. 608-615. http://geodesic.mathdoc.fr/item/NANO_2019_10_6_a0/