I have a quick question regarding the normalisation of the wave function of a particle incident on a potential barrier specifically regarding the normalisation of the wave functions.

The problem is set up as on this webpage:

https://www.ntmdt.com/spm-basics/view/tunneling-effect

And through consideration of the boundary conditions (continuity of wave function and derivative of wave function) the final wave function looks like this:

My question is: are the wave functions either side of the barrier normalisable? And if not does this mean the situation is not physical?

## Best Answer

They are not normalisable because they either come from, or extend to infinity. This essentially means that the probability density blows off and gives non-physical results.