- 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 :frac{hbar^2}{2 m} frac{d^2 R(r)}{dr^2} + [E-V_{eff}(r)] R(r) = 0 where the effective potential is given by:V_{ extrm{eff(r)=V(r)-frac{l(l+1)hbar^2}{2mr^2}the eigenenergies and the wave function behaviour obtained are different from real solution.In
1937 , R.E. Langer suggested a correction:l(l+1) ightarrow left(l+frac{1}{2} ight)^2which 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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