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,

- which means
- which means
- neglect higher order terms

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

- bound states
- tunnelling

source

psfile jl@crush.caltech.edu index

high_energy_scattering

WKB_connection_formula

perturbation_theory

WKB_bound_state

WKB_tunnelling

WKB_hydrogen