Sample questions for exam 2
(Difference between revisions)
| Line 8: | Line 8: | ||
| − | 3) Consider a particle passing over a rectangular potential barrier from left to right. Write down the general form of <math>\Psi(x)</math> 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 | + | 3) Consider a particle passing over a rectangular potential barrier from left to right. Write down the general form of <math>\Psi(x)</math> 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 | 4) For a particle in a box, show that the fractional difference in energy between adjacent eigenvalues is | ||
<math>\frac{\Delta E_n}{E_n} = \frac{2n+1}{n^2}</math> | <math>\frac{\Delta E_n}{E_n} = \frac{2n+1}{n^2}</math> | ||
Revision as of 18:08, 28 February 2008
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
