Franz Schwabl Quantum Mechanics 4th Edit · Problem 3.13

The Uncertainty Relation

Physics — Quantum Mechanics · transmission-coefficient-potential-barrier

Problem

Compute the transmission coefficient for the potential barrier

V(x) = \begin{cases} V_0 & \text{for } |x| \leq a \\ 0 & \text{for } |x| > a \end{cases}

if the energy

E

exceeds the height

V_0

of the barrier. Plot the transmission coefficient as a function of

E/V_0

(up to

E/V_0 = 3

) for

\sqrt{2mV_0 a^2/\hbar^2} = 0.75