An electron with energy E is incident upon a potential energy barrier of height E_pot

Question

An electron with energy E is incident upon a potential energy barrier of height E_pot < E and thickness L.The reflection coefficient R:

Quizplus · Accepted Answer

The reflection coefficient is given by: R = |(k1 - k2)/(k1 + k2)|^2, where k1 = sqrt(2m(E-E_pot))/hbar and k2 = sqrt(2mE_pot)/hbar are the wave numbers in regions 1 (initial) and 2 (barrier), respectively. Since E_pot < E, it follows that k2 is imaginary and the wave function in region 2 is an exponentially decaying function of position. Thus, there is a nonzero probability that the electron will be reflected back into region 1, and hence the reflection coefficient is generally not equal to zero.

An Electron with Energy E Is Incident Upon a Potential