The wave function of a two-level atomic system with states a) and ) can be expressed as: (t) = Calae-iEat/h + cbbe-lEbt/

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The Wave Function Of A Two Level Atomic System With States A And Can Be Expressed As T Calae Ieat H Cbbe Lebt 1 (44.49 KiB) Viewed 36 times

The wave function of a two-level atomic system with states a) and ) can be expressed as: (t) = Calae-iEat/h + cbbe-lEbt/h If a monochromatic wave with frequency w interacts with this two-level system and we apply the rotating wave approximation, the following set of coupled differential equations for the coefficients Ca and co is obtained: 。-iwo¹ Cb Ca = Hab e i Cb === Ha elot Ca ħ Where Hab=abelt and Hbabe-it = Now, if H' (t) is the perturbation Hamiltonian that has a sinusoidal time dependence with frequency w such that H'(r, t) = V(r)cos (wt) Hab = Vabcos (wt) Vab = (a|V|Wb) solve the coupled differential equations for ca and ch to obtain C and C given that the initial conditions at time, t= 0, are: ca (0) = 1 and c₂ (0) = 0. Express your solutions for Ca(t) and cb (t) in terms of the Rabi flopping frequency Wellgo /(w - wo)² + (Vabl/h)².