p137bp7 - Physics 137B Fall 2004 Problem set 7 resonance...

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Physics 137B, Fall 2004 Problem set 7 : resonance; adiabatic approximation Assigned Friday, 19 October. Due in box Friday, 26 October. 1. The energy difference between the n = 1 and n = 2 electronic levels of a hydrogen atom is ¯ ba = (3 / 4) × 13 . 6 eV. (a) What angular frequency (in units of s - 1 ) should an applied periodic perturbation have in order to resonantly drive transitions between an n = 1 level and an n = 2 level? (b) Suppose that the applied perturbation is an electric field in the ˆx direction: for t 0, H 0 ( t ) = - eEx sin( ωt ) . (1) To first order, will this perturbation create transitions from the ground state 1 s to the 2 s state? Why or why not? Hint: what is the “matrix element” H 0 ba ( t ) in this case? 2. Rabi flopping : Derive equations 9.70a and 9.70b in Bransden for yourself. Then do Bransden problem 9.7 (solving a simplified form of these equations–the “rotating wave” approximation). 3. Bransden 9.6. (The point is to work through the series of arguments leading to the Golden Rule
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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 Berkeley.

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