Unformatted text preview: ˆx is incident on the atom. If the system is initially in a state with harmonic oscillator quantum numbers n x ,n y ,n z , and energy E = ¯ hω (3 / 2 + n x + n y + n z ) (2) where ω is the classical oscillation frequency p k/m , what transitions are allowed within the dipole approximation? Hint: your goal is to ﬁnd which states n x ,n y ,n z have  D x ba  2 6 = 0. It may help to think about how x is expressed in terms of the raising and lowering operators for the harmonic oscillator. 4. Bransden 11.8. (Hint: Proving this “ThomasReicheKuhn sum rule” is a little tricky. It may help you to think about how the action of the expression ∑ k  ψ k i E k h ψ k  on a state is exactly the same as that of an operator you know well, and to remember that ∑ k  ψ k ih ψ k  is the identity operator.) 5. Bransden 13.2. The “laboratory coordinate system” means the one in which B particles are initially stationary. 1...
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 Fall '07
 MOORE
 Physics, mechanics, Atom, NZ, Fundamental physics concepts

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