Exponentials or trig functions for finite square well?

[baouba]

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

 

[stevendaryl]

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

The two approaches are equivalent. The point of using sines and cosines is to get a complete basis that is either even or odd under the transformation $x \Rightarrow -x$. But it really doesn't make much difference.

For infinite square wells, using sines is convenient because you can easily make the wave function zero at the two boundary points by choosing a basis function of the form $sin(kx)$ where $k = \frac{n \pi}{L}$.

 

[DeldotB]

From my experience, exponentials seem to be a little easier especially when finding transmission and reflection coefficients (but as steven daryl said: they are completely equivelant)