The WKB approximation is useful to obtain solutions to the one-dimensional time-independ...

The WKB approximation is useful to obtain solutions to the one-dimensional time-independent Schrödinger equation in cases where E ? V(x) and the potential V(x) changes slowly and gradually with x. In this case the wavelength λ (x) varies with x because of the V(x) dependence on x. (a) Argue that we can write the wavelength as

for a particle of mass m in a potential V(x). (b) By considering the number of oscillations that can be fi t

into a distance dx, show that the following equation is valid, where n is an integer and represents the number of standing waves that fi t inside the potential well.

where n is an integer (6.74) This is the WKB approximation. (Hint: the equation might be helpful)