Rotating-wave approximation: Difference between revisions

Revision as of 14:58, 13 April 2008

Revision as of 15:05, 13 April 2008

Line 105:

&= |\text{e}\rangle\langle\text{g}| + i\omega_0t|\text{e}\rangle\langle\text{g}| + \ldots \\

&= (1 + i\omega_0t + \ldots)|\text{e}\rangle\langle\text{g}| \\

&= e^{i\omega_0t}|\text{e}\rangle\langle\text{g}| ,. \\

\end{align}</math>

Operating from the left on the second term of <math>H</math> above yields zero by orthogonality of <math>|\text{g}\rangle</math> and <math>|\text{e}\rangle</math>, and the same results apply to the operation of the second exponential from the right. Thus, the new Hamiltonian becomes

so the new Hamiltonian becomes

<math>\begin{align}