Logarithmic perturbation theory: Applications and limitations

Abstract

The time independent, non-degenerate standard perturbation theory is compared the alternate treatment of perturbation theory called logarithmic perturbation theory (LPT). For determining the non-degenerate ground state the LPT is, in principle, easier to apply than standard perturbation theory. This is because, as opposed to the standard perturbation method which requires the knowledge of the complete set of eigenvalues and eigenfunctions of the unperturbed system, for the LPT one only needs to know the ground state wave function of the unperturbed system, the energy correction to the next lower order and some easily computable coupling constants. However, in reality, the LPT is a simpler method to apply when the ground state wavefunction is exponential in nature. But as shown here for trigonometric unperturbed wave function the LPT leads to integrals which have no analytical solutions thereby making LPT more difficult and less accurate method than the standard perturbation approach. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 595-600