Journal
FEW-BODY SYSTEMS
Volume 54, Issue 11, Pages 2113-2124Publisher
SPRINGER WIEN
DOI: 10.1007/s00601-013-0720-3
Keywords
-
Categories
Funding
- Theoretical Physics Laboratory of the USTHB university of Alger
Ask authors/readers for more resources
We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| (m) with m a parts per thousand yen 1 in the D = 1 dimensional space, to 1/r (m) with m a parts per thousand yen 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available