Comments about the boundary condition for reduced radial wave function in multi-dimensional equation

2022/05/30 by Anzor Khelashvili, Khelashvili, Anzor, Teimuraz Nadareishvili +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2206.00038

openalex publication_date 2022/05/30 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet condition, which seems as natural, is not mathematically well justified, on the contrary to the 3-dimensional case. The stronger argument in favour of Dirichlet boundary condition is the requirement of time independence of wave functions norm. The problem remains open for singular potentials.

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