Schrödinger equation in one dimension is considered.
The force is approximated by a special double well, quasi-exactly solvable at zero energy.
The liouvillean change of variables then maps the related Laguerre-polynomial zero-order wavefunction on an N-th harmonic-oscillator state.
Key step: The backward mapping converts then the usual oscillator basis into Sturmians.
All corrections are then easily defined by formulae which generalize the textbook ones.
Published in J. Math. Phys. 38 (1997) 5087 - 5097.