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

G. Muchatibaya; S. Fassari; F. Rinaldi; J. Mushanyu

doi:10.1155/2016/2125769

Advances in Mathematical Physics (Jan 2016)

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

G. Muchatibaya,
S. Fassari,
F. Rinaldi,
J. Mushanyu

Affiliations

G. Muchatibaya: Department of Mathematics, University of Zimbabwe, P.O. Box MP167, Mount Pleasant, Harare, Zimbabwe
S. Fassari: Universitá Degli Studi Guglielmo Marconi, Via Plinio 44, 00193 Rome, Italy
F. Rinaldi: Universitá Degli Studi Guglielmo Marconi, Via Plinio 44, 00193 Rome, Italy
J. Mushanyu: Department of Mathematics, University of Zimbabwe, P.O. Box MP167, Mount Pleasant, Harare, Zimbabwe

DOI: https://doi.org/10.1155/2016/2125769
Journal volume & issue: Vol. 2016

Abstract

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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.

Published in Advances in Mathematical Physics

ISSN: 1687-9120 (Print); 1687-9139 (Online)
Publisher: Wiley
Country of publisher: United Kingdom
LCC subjects: Science: Physics
Website: https://onlinelibrary.wiley.com/journal/3197

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