Abstract
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.
| Original language | English |
|---|---|
| Article number | 83 |
| Journal | European Physical Journal Plus |
| Volume | 133 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Mar 2018 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity. / Ishkhanyan, A. M.
In: European Physical Journal Plus, Vol. 133, No. 3, 83, 01.03.2018.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
AU - Ishkhanyan, A. M.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.
AB - We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential, which belongs to a general Heun family, is a short-range one that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. We derive the exact spectrum equation for the energy and discuss the bound states supported by the potential.
UR - http://www.scopus.com/inward/record.url?scp=85042709629&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042709629&partnerID=8YFLogxK
U2 - 10.1140/epjp/i2018-11912-5
DO - 10.1140/epjp/i2018-11912-5
M3 - Article
AN - SCOPUS:85042709629
VL - 133
JO - European Physical Journal Plus
JF - European Physical Journal Plus
SN - 2190-5444
IS - 3
M1 - 83
ER -