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

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.