https://doi.org/10.1140/epjc/s10052-017-5362-z
Regular Article - Theoretical Physics
Highly excited bound-state resonances of short-range inverse power-law potentials
1
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2
The Hadassah Academic College, 91010, Jerusalem, Israel
* e-mail: shaharhod@gmail.com
Received:
24
July
2017
Accepted:
3
November
2017
Published online:
17
November
2017
We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form 
with 
. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy 
, which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.
© The Author(s), 2017
