Fine Theoretical Physics Institute Seminar

A simple approximation of the ground state eigenfunction for both
the quantum-mechanical anharmonic oscillator and the double-well
potential given by V = m2x2 + gx4 at arbitrary g≥0 for
m2≥0 and m2 < 0 , respectively, is proposed. The approximation models perturbation theory results at small distances and WKB asymptotics at large distances. It is shown that this approximation if taken as variational trial function defines the energies of low-lying states with relative accuracy 10 ^{- 8} - 10 ^{- 10} even in semiclassical domain. It is also shown that this approximation if taken as zero approximation
for solving the Schroedinger equation leads to an extremely fast convergent perturbation theory. A generalization to multidimensional anharmonic oscillators is briefly discussed.