In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to escape the potential through a process call quantum tunneling.
This seems extraordinary from the point of classical mechanics because it implies the particle must cross a zone where it has imaginary momentum. I understand that from the point of view of quantum mechanics there is a non zero probability for the particle to be in such zones.
What is it know about the behaviour of the particle in this zone?
Links to research experiments or papers would be appreciated.
Best Answer
I can give you one example. In a semiconductor reverse-biased p-n junction, a potential barrier exists that prevents electrons from crossing the junction. There is an energetically-forbidden region in the vicinity of the junction. The wave functions of electron states in both the valence and conduction bands are real exponential in this region. Additionally it's possible that the only spatial overlap between the valance and conduction bands occurs in the forbidden region. Yet optical absorption occurs due to valance to conduction band transitions. The interpretation is that electrons in the forbidden region are promoted from the exponential tail of the valence band to the exponential tail of the conduction band. This process is called the Franz-Keldysh effect or tunneling-assisted absorption.
Here's a nice figure from the German Wikipedia page. The English page doesn't have such a nice figure.