The Langer correction is a correction when WKB approximation

WKB approximation

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients...

 method is applied to three-dimensional problems with spherical symmetry.

When applying WKB approximation method to the radial Schrödinger equation

Schrödinger equation

The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

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

WKB approximation

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients...

reproduces the exact spectrum for many potentials.