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Jaynes-Cummings Model Lagrangian

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to write down the path integral for the Jaynes-Cummings Model which involves obtaining the Lagrangian.

    2. Relevant equations

    [tex]\hat{H}_{\text{JC}} = \hbar \nu \hat{a}^{\dagger}\hat{a} +\hbar \omega \frac{\hat{\sigma}_z}{2} +\frac{\hbar \Omega}{2} \left(\hat{a}\hat{\sigma}_+ +\hat{a}^{\dagger}\hat{\sigma}_-\right)[/tex]

    3. The attempt at a solution

    To get the Lagrangian from the Hamiltonian is it reasonable to write the creation and annihilation operators in terms of x and p, solve
    [tex]\dot{x}=\frac{\partial H(x,p)}{\partial p}[/tex]
    for p and plug this into
    [tex]L(x,\dot{x};t)=\dot{x}p−H(x,p;t)[/tex]?
     
  2. jcsd
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