[en] The nature of the bound state energies and wave functions of the Schroedinger equation with the potential V=A/x²+Bx² is investigated in detail by attempting a numerical solution to the problem. We report some interesting results which some of the earlier workers could not get. It is found contrary to the previous report that for A<-h²/8m there are well defined bound states. The addition of the term A/x² to the one dimensional oscillator potential lowers the symmetry of the eigen states for negative values of A and for positive values of A the eigen states become degenerate with respect to parity. (author). 6 refs, 4 tabs