WKB=(Wentzel,Kramers,Brillouin, 1926) Approximation = classical approximation.

A semi-classical method for solving 1-d schrodinger approximation.

valid when de Broglie wavelength changes slowly: tex2html_wrap148 . tex2html_wrap149 small when h- tex2html_wrap150 0, m- tex2html_wrap150 0, p- tex2html_wrap150 tex2html_wrap153 or when tex2html_wrap154 - tex2html_wrap150 0.

WKB doesn't work at the classical turning points.

Formal expansion:

Schrodinger equation: tex2html_wrap156 so tex2html_wrap157 for tex2html_wrap158 .

V= constant - tex2html_wrap150 k=constant, tex2html_wrap160 .

if V not a constant, try tex2html_wrap161 This gives the equation: tex2html_wrap162 .

The expansion as tex2html_wrap163 is tex2html_wrap164 .

plugging back into the equation, you get: tex2html_wrap165 .

each coefficient must seperately go to 0 so,

Then tex2html_wrap170 tex2html_wrap171

works in both classically allowed and forbidden regions as long as tex2html_wrap172 E-V tex2html_wrap172 tex2html_wrap150 tex2html_wrap150 0

In forbidden regions: tex2html_wrap176 tex2html_wrap177

Example: high energy scattering off of attractive potential

There are applications to




source
psfile jl@crush.caltech.edu index
high_energy_scattering
WKB_connection_formula
perturbation_theory
WKB_bound_state
WKB_tunnelling
WKB_hydrogen