Please provide step by step solution with formulas and
explanation. Source: Griffith's Time-dependent Perturbation Theory.
Answer only b, c, d.
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Please Provide Step By Step Solution With Formulas And Explanation Source Griffith S Time Dependent Perturbation Theor 1 (54.21 KiB) Viewed 13 times
Please Provide Step By Step Solution With Formulas And Explanation Source Griffith S Time Dependent Perturbation Theor 2 (93.73 KiB) Viewed 13 times
** Problem 9.14 Develop time-dependent perturbation theory for a multilevel sys- tem, starting with the generalization of Equations 9.1 and 9.2: Hown = E.V. (11m) = Ohm [9.79] At time t = 0 we turn on a perturbation H'(t), so that the total Hamiltonian is H = H + H'(t). [9.80] (a) Generalize Equation 9.6 to read "(t) = { cm(t)\ne-it/ (9.81) and show that C. - [9.82] where = (m H'IV.). [9.83] (b) If the system starts out in the state n, show that (in first-order perturbation theory) en(1) 1 [9.84) * Çok_elEn-E.sk Á Hvx(") di h
and i Cm(t) =- S Lx'belen-Eww! di', (m + N). [9.85) ņi (C) For example, suppose H' is constant (except that it was turned on at t = 0 and switched off again at some later time t). Find the probability of transition from state N to state m (m + N), as a function of t. Answer: (Ey ] [9.86] (EN - Em) 41 14x12 sin’ſ(Ex – Em)1/21] (d) Now suppose H' is a sinusoidal function of time: H = V cos(wt). Making the usual assumptions, show that transitions occur only to states with energy Em = Ep +hw, and the transition probability is , sinºt(EN - Em thú); /2h) Py>m= 1Vm012 [9.87] (EN - Em ħw)2
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