Question

Figure 5.12 on page 159 of the modern physics book shows the finite well. Is it your interpretation that you can find the particle outside of the well? How would this situation possibly be manifested in a real-life experiment?

Answer 1

According to quantum interpretation, there is a non-zero probability of the particle being outside the well even when the energy of the particle is less than the potential energy barrier of the walls. This phenomenon is know as Quantum tunnelling or tunneling. Heisenberg uncertainty principle defines a limit on how precisely the position and the momentum of a particle can be known at the same time.This implies that there are no solutions with a probability of exactly zero or one. Hence, the probability of a given particle's presence outside the well is non-zero.

Applications -

Quantum tunnelling is essential for nuclear fusion in stars to overcome the Coulomb barrier in order to achieve a thermonuclear fusion.

Emission of particles and energy from the unstable nucleus of an atom to form a stable product(Radioactive decay) is done via the tunnelling of a particle out of the nucleus.