Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well
type: Item
instance of: scholarly article
title: Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well
zbMATH Open document ID: 1304.81069
DOI: 10.1063/1.4894057
author: Piotr Garbaczewski
author: Mariusz Żaba
published in: Journal of Mathematical Physics
publication date: 2014-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1403.5668
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6358476
zbMATH Keywords: nonl-ocal Schrödinger operator
zbMATH Keywords: Cauchy oscillator
zbMATH Keywords: Cauchy well
zbMATH Keywords: spectral problems
zbMATH Keywords: Strang method
MaRDI profile type: Publication
OpenAlex ID: W3098058822
arXiv ID: 1403.5668
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review text: The authors present the results of a computer-assisted route to obtain the eigenvalues and the eigenfunctions of the \(1D\) Cauchy-Schrödinger operator \(H=(-\Delta)^{1/2} + V\), \(V\) being a local potential. The Cauchy oscillator (which also has an analytical solution) and Cauchy finite well spectral problems are mainly envisaged. The algorithms employed are a non-local version of Strang's splitting method, which is based on Trotter product formula.
reviewed by: Mihai Pascu
description: scientific article; zbMATH DE number 6358476