Exact solutions for the Schrödinger equation with a conditionally integrable potential of x^{2/3} attractive plus fixed x^{-2} repulsive terms are given in terms of non-integer Hermite functions.
New conditionally exactly solvable potentials of exponential type
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Based on a method that produces the solutions to the Schrodinger equations of partner potentials, we give two conditionally exactly solvable partner potentials of exponential type defined on the half line. These potentials are multiplicative shape invariant and each of their linearly independent solution includes a sum of two hypergeometric functions. Furthermore we calculate the scattering amplitudes and study some of their properties.
fields
quant-ph 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
A Schr\"odinger potential involving $x^\frac{2}{3}$ and centrifugal-barrier terms conditionally integrable in terms of the confluent hypergeometric functions
Exact solutions for the Schrödinger equation with a conditionally integrable potential of x^{2/3} attractive plus fixed x^{-2} repulsive terms are given in terms of non-integer Hermite functions.