Sample questions for exam 2

1) A particle is incident from the left with energy E > V₀. Compute the reflection coefficient.

2) Match the figures on the left, with the appropriate one on the right

3) Consider a particle passing over a rectangular potential barrier from left to right. Write down the general form of Ψ(x) in the three regions. Then use the boundary conditions to derive 4 equations for the 5 unknown coefficients. For 10 bonus points, use these 4 equations to derive the transmission coefficient.

4) For a particle in a box, show that the fractional difference in energy between adjacent eigenvalues is

$\frac{\Delta E_n}{E_n} = \frac{2n+1}{n^2}$