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# ps5a - w Quantum Mechanics II(G4022 — Spring 2009...

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Unformatted text preview: w. Quantum Mechanics II (G4022 — Spring 2009) Solutions: Problem Set 5 Prof. A. Mueller TA: Fabio Dominguez 1. 15.1. The perturbation is given by V(t)={0 t<0 (1) (”Ema—7‘ t > 0 Since we are interested in calculating transitions between the 13 and the 2p levels, we have to Calculate the matrix element of the form (100|V(t)|2lm) = eEge’ltﬂOszlﬂm) (2) : ee-Eo / d?» wroomzwmmm (3) = CEoe—pyt (100 dr 7'3R10(7‘)R21(T')> (/ d9 3166(9, Cb) COS 0Km(6a Q») (4) Lets focus on the angular integral. The only <15 dependence comes from the Yzhn factor and therefore is of the form 6”“. Therefore the matrix element is zero unless m = 0. In this case we have _ * 1 3 /d9 WM) max/low, (15) = /dn Ecosggcosﬂ \ (5) i 1- : g/ d(cos t9) c0526 (6) —1 1 = __ 7 \/§ ( ) The radial integral gives foo (17' r3R10(r)R21(r) : /30 dr r3——1—26'T/“° 1 T e_T/2“° (8) 0 0 0.3/2 (2a0)3/2 x/gao 1 0° 4 3 /2 = dr 7 T a" 9 «as f r e < > :n 29/2a0 0° 4 _u I 'éﬁfaq‘w}? = 311/2 A duu e (10) fC, __ 215/2a0 ...
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