Unformatted text preview: 2. (a) What is the density of states ρ ( E ) of a 1D harmonic oscillator of frequency ω ? Hint: ﬁrst calculate N ( E ), the number of states of energy less than E , and replace the resulting steplike function by a continuous (in this case, linear) function that agrees on average when N is large. Then use ρ ( E ) = dN/dE . (b) What is the density of states of a 2D harmonic oscillator? You should start by convincing yourself that the energy levels are, for nonnegative integers n x and n y , E n x ,n y = ¯ hω (1 + n x + n y ) . (3) 3. Bransden 9.1. (The goal is to calculate the total transition probability out of the ground state from this perturbation.) 4. Check your answer to problem 3 in the limit τ → ∞ by using the sudden approximation. (Hint: can you make the ﬁnal Hamiltonian into another harmonic oscillator?) 1...
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 Fall '07
 MOORE
 Physics, mechanics, Enx, Timedependent perturbation theory, sudden approximation

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