A Note on the Discrete Spectrum of Gaussian Wells (I): The Ground State Energy in One Dimension

The ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root.

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Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2016; no. 2016; pp. 149 - 152
Main Authors Mushanyu, J., Rinaldi, F., Fassari, S., Muchatibaya, G.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2016
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Approximation
Colleges & universities
Fourier transforms
Gaussian processes
Ground state
Helium
Mathematical research
Operator theory
Physics research
Spectrum analysis
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Summary:The ground state energy E0(λ) of Hλ=-d2/dx2-λe-x2 is computed for small values of λ by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which ϵ0(λ)=|E0(λ)|1/2 is the root.
ISSN:1687-9120
1687-9139
DOI:10.1155/2016/2125769