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

<math> -frac frac + R(r) = 0 </math>

where the effective potential is given by

<math>V_(r)=V(r)-frac</math>

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

In 1937, Rudolph E. Langer suggested a correction

<math>l(l+1) rightarrow left(l+fracright)^2</math>

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.

References

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