FERMIS GOLDEN-RULE AND BARDEENS TUNNELING THEORY

A simple way to derive Bardeen's tunneling theory is introduced. With a low rate of tunneling of, for example, electrons from one electrode to another through a wide vacuum gap, the appearance of the second ele ctrode can be regarded as a perturbation. Then Bardeen's formula for t unneling follows exactly from Fermi's golden rule, supposing that this perturbation appears suddenly at some instant of time. Bardeen's theo ry is illustrated by assuming a smoothly variable barrier shape, inclu ding the rectangular one as a limiting case. This exactly solvable exa mple clarifies the sensitivity of the tunneling probability to the bar rier shape and the energy of the tunneling particle. (C) 1995 American Association of Physics Teachers.