The probability density for the region of a square well of width L, and

, drops off exponentially according to

where C is a constant. (a) We have to show that the wave function is a solution of the one-dimensional form of the Schrödinger’s equation, and have to find the value of k for this to be true.

Solution:             Click For PDF Version

The one-dimensional Schrödinger equation for a particle of mass m, energy E, moving in the square well potential

, in the region will be

If we have .

Substituting in the Schrödinger equation given above, we get

This implies that