**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.**