The presence of non-analyticities and singularities in the wavefunction and the role of invisible delta potentials

• URL: http://arxiv.org/abs/2012.00166v1
• Date: Mon, 30 Nov 2020 23:37:00 GMT
• Title: The presence of non-analyticities and singularities in the wavefunction and the role of invisible delta potentials
• Authors: Jorge Munzenmayer and Derek Frydel
• Abstract summary: We identify the correct differential equation for a divergent square-integrable solution. We infer that the divergent wavefunction would be caused by the potential V(r)=-r(r) Because of its peculiar form and the fact that it leads to a divergent potential energy V> = infinity, the potential V(r) and the divergent wavefunction associated with it are not physically meaningful.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the singularity there is no underlying physical cause, therefore, the divergence would have to be a nonlocal phenomenon caused by confining walls at a distance. In this work we examine this claim more carefully. By identifying the correct differential equation for a divergent square-integrable solution and rewriting it in the form of the Schroedinger equation, we infer that the divergent wavefunction would be caused by the potential V(r)=-r delta(r), which is a kind of attractive delta potential. Because of its peculiar form and the fact that it leads to a divergent potential energy <V> = - infinity, the potential V(r) and the divergent wavefunction associated with it are not physically meaningful.

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