Quantum anharmonic oscillators: a new approach
  The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schroedinger equation which are regular respectively at the origin and at infinity. We show in this paper how to evaluate that Wronskian exactly, except for numerical rounding errors. The procedure is illustrated by application to the gx2+x2N (N a positive integer) oscillator. 
F. J. Gomez and J. Sesma