Energy levels of a nonpolynomial oscillator using finite difference technique

The energy levels of a one-dimensional system are calculated for the rational potentials V1(x;N,λ,g) = x2 + λx2N(1 + gx2) and V2∓(x;μ,I,N,M,g,α) = μx2I∓gx2N(1 + gαx2M), using the finite difference approach over wide range of values of the perturbation parameters (λ,g,μ,α,I,N,M) and for various state numbers n. The numerical results are compared with previous numerical data and with available exact values.