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dc.contributor.authorMushtaq, Asif
dc.contributor.authorNoreen, Amna
dc.contributor.authorOlaussen, Kåre
dc.date.accessioned2021-02-17T12:25:45Z
dc.date.available2021-02-17T12:25:45Z
dc.date.created2020-09-29T11:13:05Z
dc.date.issued2020
dc.identifier.citationMushtaq, A., Noreen, A. & Olaussen, K. (2020). Numerical Solutions of Quantum Mechanical Eigenvalue Problems. Frontiers in Physics, 8: 390. doi:en_US
dc.identifier.issn2296-424X
dc.identifier.urihttps://hdl.handle.net/11250/2728676
dc.description.abstractA large class of problems in quantum physics involve solution of the time independent Schrödinger equation in one or more space dimensions. These are boundary value problems, which in many cases only have solutions for specific (quantized) values of the total energy. In this article we describe a Python package that “automagically” transforms an analytically formulated Quantum Mechanical eigenvalue problem to a numerical form which can be handled by existing (or novel) numerical solvers. We illustrate some uses of this package. The problem is specified in terms of a small set of parameters and selectors (all provided with default values) that are easy to modify, and should be straightforward to interpret. From this the numerical details required by the solver is generated by the package, and the selected numerical solver is executed. In all cases the spatial continuum is replaced by a finite rectangular lattice. We compare common stensil discretizations of the Laplace operator with formulations involving Fast Fourier (and related trigonometric) Transforms. The numerical solutions are based on the NumPy and SciPy packages for Python 3, in particular routines from the scipy.linalg, scipy.sparse.linalg, and scipy.fftpack libraries. These, like most Python resources, are freely available for Linux, MacOS, and MSWindows. We demonstrate that some interesting problems, like the lowest eigenvalues of anharmonic oscillators, can be solved quite accurately in up to three space dimensions on a modern laptop—with some patience in the 3-dimensional case. We demonstrate that a reduction in the lattice distance, for a fixed the spatial volume, does not necessarily lead to more accurate results: A smaller lattice length increases the spectral width of the lattice Laplace operator, which in turn leads to an enhanced amplification of the numerical noise generated by round-off errors.en_US
dc.language.isoengen_US
dc.publisherFrontiersen_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.no*
dc.titleNumerical Solutions of Quantum Mechanical Eigenvalue Problemsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionpublishedVersionen_US
dc.rights.holder© 2020 The Author(s)en_US
dc.subject.nsiVDP::Matematikk og Naturvitenskap: 400::Fysikk: 430en_US
dc.source.pagenumber10en_US
dc.source.volume8en_US
dc.source.journalFrontiers in Physicsen_US
dc.identifier.doi10.3389/fphy.2020.00390
dc.identifier.cristin1834731
dc.description.localcodeUnit Licence Agreementen_US
dc.source.articlenumber390en_US


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