Under an entirely misleading title one finds just an easy
illustrative example of the so called quasi-exactly solvable
Schroedinger equation. The message is promptly reproduced when one
takes any wave function from Tables 2 or 3 and differentiates it
twice. The corresponding potential is then obtained via eq. (6).
Recommended reading: A. Ushveridze, Quasi-exactly solvable models in
Quantum Mechanics, IOP, Bristol, 1994.


MR2396773 Ye\c silta\c s, Özlem; Ocak, S. Bilge
The generalized $PT$-symmetric sinh-Gordon potential solvable
within quantum Hamilton-Jacobi formalism.
Internat. J. Theoret. Phys. 47 (2008), no. 2, 415--420. 81Q10