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.
Solving a two-electron quantum dot model in terms of polynomial solutions of a bi-confluent Heun equation
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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.