A note on the discrete spectrum of Gaussian wells. I: The ground state energy in one dimension
type: Item
instance of: scholarly article
title: A note on the discrete spectrum of Gaussian wells. I: The ground state energy in one dimension
zbMATH Open document ID: 1400.82147
DOI: 10.1155/2016/2125769
published in: Advances in Mathematical Physics
publication date: 2018-10-17T00:00:00Z
review text: Summary: The ground state energy \(E_0(\lambda)\) of \(H_\lambda = - d^2 / d x^2 - \lambda e^{- x^2}\) is computed for small values of \(\lambda\) by means of an approximation of an integral operator in momentum space. Such an approximation leads to a transcendental equation for which \(\epsilon_0(\lambda) = | E_0(\lambda) |^{1 / 2}\) is the root.
Mathematics Subject Classification ID: 82C10
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 65L15
zbMATH DE Number: 6957362
zbMATH Keywords: Gaussian wells
zbMATH Keywords: ground state energy
author: Gift Muchatibaya
author: Silvestro Fassari
author: Fabio Rinaldi
author: Josiah Mushanyu
MaRDI profile type: Publication
Wikidata QID: Q59122198
full work available at URL: https://doi.org/10.1155/2016/2125769
OpenAlex ID: W2292583541
cites work: On the spectrum of the Schrödinger Hamiltonian with a particular configuration of three one-dimensional point interactions
cites work: On the bound state of Schrödinger operators in one dimension
cites work: The bound state of weakly coupled Schrödinger operators in one and two dimensions
cites work: Computing eigenvalues of singular Sturm-Liouville problems
cites work: Titchmarsh–Weyl theory and its relations to scattering theory: Spectral densities and cross sections; Theory and applications
cites work: On the asymptotic form of the Titchmarsh-Weylm-coefficient†
cites work: Q4864494
cites work: Q4191141
cites work: A note on the eigenvalues of the Hamiltonian of the harmonic oscillator perturbed by the potential \(\lambda x^2/(1+gx^2)\)
cites work: On the interaction of the type λx2/(1+g x2)
cites work: Algorithm 810: The SLEIGN2 Sturm-Liouville Code
description: scientific article; zbMATH DE number 6957362