Transitions Between Levels Spaced Almost Continuously

Abstract

The transition probabilities between closely spaced energy levels, when calculated according to the usual perturbation methods, lead to apparent infinities if the perturbation is finite. A more appropriate method of approximation which disposes of the infinities is worked out. The resulting finite transition probabilities are identical with the finite parts of the usual expressions in first and second order, but additional finite terms appear in orders higher than the second