Two-well oscillator

Very accurate eigenvalues of the two-well oscillator ($H(k, \lambda )=p^2-k{x}^2+\lambda x^4$) are obtained by a nonperturbative method. The splitting between the paris of lower eigenvalues is found to be remarkably well estimated by the WKB approximation. It is observed that the scaling properties of the exact eigenvalues with respect to the parameters in the Hamiltonian are retained in the WKB approximation.