Langer Correction

The Langer correction is a correction when WKB approximation method is applied to three-dimensional problems with spherical symmetry.

When applying WKB approximation method to the radial Schrödinger equation

where the effective potential is given by

the eigenenergies and the wave function behaviour obtained are different from real solution.

In 1937, Rudolph E. Langer suggested a correction

which is known as Langer correction. This is equivalent to inserting a 1/4 constant factor whenever l(l+1) appears. Heuristically, it is said that this factor arises because the range of the radial Schrödinger equation is restricted from 0 to infinity, as opposed to the entire real line.

By such a changing of constant term in the effective potential, the results obtained by WKB approximation reproduces the exact spectrum for many potentials.

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