Question

Solve the shrodinger wave equation using WKB approximate ?

Answer 1

solution :

Main idea of WKB approximate is ,If potential V is constant and energy E of the particle is E>V, then the particle wave function has the form

...Equ(1)

+ sign indicate particle is travelling to the right , and - for left

And General solution is a linear superposition of the two.

and also The wave function is oscillatory with a fixed wavelength and fixed amplitude A.

So we take a solution at turning points when V ≈ E

the classical region (solution of SWE in this region)

or

where .......Equ (2)

We assume for now that E>V (x) and p is real.

ψ is some complex function, and therefore can be expressed as

....Eua (3)

where A(x) is amplitude and = phase

putting Euation (3)in Equ 2 we get