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.
A conditionally exactly solvable generalization of the potential step
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abstract
Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we obtain that each linearly independent solution of the Schrodinger equation includes two hypergeometric functions. Furthermore we calculate their reflection and transmission amplitudes. Finally we discuss some additional properties of these potentials.
fields
quant-ph 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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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.