The Coulomb potential in quantum mechanics revisited
Abstract
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at r = 0 and r → ∞ are considered. We highlight this fact by solving a model for the Coulomb potential with a cutoff (representing the finite extent of the nucleus). In the limit that the cutoff is reduced to zero, we recover the standard result, albeit in a nonstandard way. This example is used to emphasize that a more consistent approach to solving the Coulomb problem in quantum mechanics requires an examination of the nonstandard solution. The end result is, of course, the same.
 Publication:

American Journal of Physics
 Pub Date:
 May 2017
 DOI:
 10.1119/1.4976829
 arXiv:
 arXiv:1612.06706
 Bibcode:
 2017AmJPh..85..346O
 Keywords:

 Physics  General Physics
 EPrint:
 7 pages 5 figures