2020/11/30 by Jorge Munzenmayer, Munzenmayer, Jorge, Derek Frydel +1
Chemistry · Earth and Planetary Sciences · Physics and Astronomy · #Electrostatics and Colloid Interactions #FOS: Physical sciences #Geophysical and Geoelectrical Methods #Nonlinear Waves and Solitons #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Soft Condensed Matter (cond-mat.soft) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2012.00166
openalex publication_date 2020/11/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001]\nthat a solution to a particle in an infinite spherical well model, if it is\nsquare-integrable, is a physically valid solution, even if at the precise\nlocation of the singularity there is no underlying physical cause, therefore,\nthe divergence would have to be a nonlocal phenomenon caused by confining walls\nat a distance. In this work we examine this claim more carefully. By\nidentifying the correct differential equation for a divergent square-integrable\nsolution and rewriting it in the form of the Schroedinger equation, we infer\nthat the divergent wavefunction would be caused by the potential V(r)=-r\ndelta(r), which is a kind of attractive delta potential. Because of its\npeculiar form and the fact that it leads to a divergent potential energy <V> =\n- infinity, the potential V(r) and the divergent wavefunction associated with\nit are not physically meaningful.\n