Convergent perturbation expansion for the anharmonic oscillator

Abstract

We study the ground state as well as the first three excited states of the anharmonic oscillator with anharmonicity λ x 4 for a range of λ = (0, 10) with the first-order logarithmic perturbation iteration method (FOLPIM). This leads to convergent results. The initial choice of the wave function seems only to affect the rate of convergence in the case of the ground state but may critically affect the convergence for the excited states. For large values of λ, convergence is best obtained by choosing the asymptotic solution as the initial “unperturbed” wave function.