Sample questions for exam 2
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1) A particle is incident from the left with energy <math>E > V_0</math>. Compute the reflection coefficient. | 1) A particle is incident from the left with energy <math>E > V_0</math>. Compute the reflection coefficient. | ||
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| + | Image:Steppotential.gif|click to see the full size picture | ||
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2) Match the figures on the left, with the appropriate one on the right | 2) Match the figures on the left, with the appropriate one on the right | ||
<gallery> | <gallery> | ||
| − | Image:Potentials_cartoon.gif| click to see the full size picture | + | Image:Potentials_cartoon.gif|click to see the full size picture |
</gallery> | </gallery> | ||
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Revision as of 18:32, 28 February 2008
1) A particle is incident from the left with energy E > V0. Compute the reflection coefficient.
click to see the full size picture
2) Match the figures on the left, with the appropriate one on the right
click to see the full size picture
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
where 
5) Apply the raising operator to the ground state wavefunction for the harmonic oscillator to construct the first excited state wavefunction. Verify by direct calculation that this function satisfies the Schrodinger equation.
