A semi-classical method for solving 1-d schrodinger approximation.
valid when de Broglie wavelength changes slowly: . small when h- 0, m- 0, p- or when - 0.
WKB doesn't work at the classical turning points.
Formal expansion:
Schrodinger equation: so for .
V= constant - k=constant, .
if V not a constant, try This gives the equation: .
The expansion as is .
plugging back into the equation, you get: .
each coefficient must seperately go to 0 so,
Then
works in both classically allowed and forbidden regions as long as E-V 0
In forbidden regions:
Example: high energy scattering off of attractive potential
There are applications to