Sample questions for exam 2
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where <math>\Delta E_n \equiv E_{n+1} - E_n</math> | where <math>\Delta E_n \equiv E_{n+1} - E_n</math> | ||
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+ | 5) Apply the raising operator <math>a^{\dag}</math> 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. |
Revision as of 18:20, 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
where
5) Apply the raising operator Failed to parse (Cannot write to or create math temp directory): a^{\dag}
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.