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 ¯ hω 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, H0 ( 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” H0 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
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 08/01/2008 for the course PHYSICS 137B taught by Professor Moore during the Fall '07 term at Berkeley.