[10 marks] The time-evolution operator in the interaction picture, T(t, to), is defined to satisfy dT iħ- =VT, Ť (to, to

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10 Marks The Time Evolution Operator In The Interaction Picture T T To Is Defined To Satisfy Dt Ih Vt T To To 1 (58.01 KiB) Viewed 23 times

[10 marks] The time-evolution operator in the interaction picture, T(t, to), is defined to satisfy dT iħ- =VT, Ť (to, to) = 1 dt where the Hamiltonian can be decomposed as Ĥ = Ho+V and V = eiHot/he-iĤot/h Show that for a quantum harmonic oscilator with Ho = p²/2m + mw²²/2, in a constant electric field so that V = -qEo, we have dŤ p ih- = qE (â cos wt + dt sin wt) T mw Using this, or otherwise, find Ï(t,0) to leading order in E.