HW 5
1. For E > V0, use the formula for the
transmission coefficient of a square barrier of height V0 and widths
L to demonstrate the first and second transmission resonances. For that you
should extract the condition under which you obtain T = 1 for this formulae,
using the appropriate wave number 
and the discrete energy levels for resonances
according to
(2 point for each demonstration).
Does the reflection coefficient increase from zero to some finite value < 1 for E > E1 and decrease to zero again for E = E2? Qualitative reasoning suffices for 1 point
2. Use https://phet.colorado.edu/sims/cheerpj/quantum-tunneling/latest/quantum-tunneling.html?simulation=quantum-tunneling to create
a) a reflection coefficients of at least 0.95 with a double ditch
b) a transmission coefficient of at least 0.95 with a single potential barrier and E > V0
c) a transmission coefficient of at least 0.95 with a single potential barrier and E < V0
by varying both the potential energy function and the length, L, of the ditch or barrier. Submit screen-shots (2 points each) as answers. Which of these three scenarios represent the wave (mechanical) phenomenon of tunneling? (1 point, i.e. 7 points in total)
3. Electrons with a kinetic energy of 5 eV tunnel through a square potential barrier with height 10 eV. Calculate the transmissions coefficients for barrier thicknesses of 1 nm and 2 nm. 2 points. Why is the transmission confident for the larger barrier thickness not simply one half of that of the thinner barrier? (Qualitative reasoning suffices, 1 point). Out of 1 billion electrons (with identical wavefunction), approximately how many will tunnel trough the 1 nm thick barrier, how many will be reflected back to where they came from, and how many electrons will get stuck in the barrier? 3 points, i.e. 8 points in total.