Quantum Mechanics

Tunneling: Thought experiment

Consider the thought experiment in which two identical wave packets start moving at the same time. The blue colored wave packet will hit a potential barrier ( ) whereas the red colored one (initially invisible because hidden under the blue wave) will not feel the step.

The wave packet that tunneled through the potential barrier (i.e. the blue wave to the right of the strip) runs ahead of the red-colored wave packet that did not feel any potential. The initial Gaussian wave packet can be viewed as a superposition of plane waves with different momentum. A tunnel barrier acts as a high-pass momentum filter: For increasing momentum perpendicular to the step, the probability for tunneling increases. This filtering effect also occurs if the motion of the particle is one-dimensional. It is a direct consequence of the fact that the tunnel probability is a function of the energy. In free space the energy is proportional to the momentum squared.