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Unformatted text preview: x 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 = h (3 / 2 + n x + n y + n z ) (2) where is the classical oscillation frequency p k/m , what transitions are allowed within the dipole approximation? Hint: your goal is to nd 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  k i E k h k  on a state is exactly the same as that of an operator you know well, and to remember that k  k ih 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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This note was uploaded on 08/01/2008 for the course PHYSICS 137B taught by Professor Moore during the Fall '07 term at University of California, Berkeley.
 Fall '07
 MOORE
 Physics, mechanics

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