The presence of nonanalyticities and singularities in the wavefunction and the role of invisible delta potentials
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 squareintegrable, 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 squareintegrable 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2012.00166
 arXiv:
 arXiv:2012.00166
 Bibcode:
 2020arXiv201200166M
 Keywords:

 Quantum Physics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 5