- #1

jameson2

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## Homework Statement

I have to evaluate [tex] P(t)=|<+,n|\exp{\frac{-iHt}{\hbar}}|+,n>|^2 [/tex] where [tex] H=\hbar \omega_0 S_z + \hbar \omega a^+a+\hbar \lambda(a^+S_-+aS_+) [/tex] and [tex] |+,n>=\left( \begin{array}{c}

1\\0 \end{array} \right) [/tex]

## Homework Equations

Eigenvalues of H are [tex] E_\pm =\hbar \omega (n +\frac{1}{2}) \pm \hbar \lambda\sqrt{n+1} [/tex] and eigenstates are [tex] |E_\pm> =\frac{1}{\sqrt{2}}(|+,n>\pm|-,n+1>) [/tex].

## The Attempt at a Solution

Basically, I don't know how to treat the hamiltonian when it's in the exponential like that. The answer is given as [tex] P(t)=cos^2(t\labda \sqrt{n+1}) [/tex] but I've no idea how to start.