A perturbation theory without energy corrections

Abstract

ABSTRACT:We employ logarithmic perturbation theory in a form that utilizes the force, instead of the potential, and yields equations for wavefunction-correction terms without requiring any information of energy corrections at any stage. The knowledge of unperturbed eigenfunctions of other states is also unnecessary. The perturbed energy eigenvalue can be obtained as a series either by going back to the parent equation, or as an average value involving the perturbed state. The latter scheme applies to any other average property as well. Both ground and excited states of a few systems are chosen for demonstrative calculations. Influence of the nodal structure on the exponential function controlling spatial behavior of the probability density is discussed. Interrelations among specific correction terms are shown in the small-and large-x regime; in the latter case, certain terms nicely sum up to yield the correct decay characteristics of the probability density as well. Relevance of the basic equation to an alternative, nonperturbative scheme of approximation is also outlined.