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DensityMatrix

< Appendices | Index | The interaction representation >

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The density matrix is an operator, hence its time evolution is dictated bythe Heisenberg equation

{$ (1) \qquad\qquad \frac {d \rho} {dt} = \frac i \hbar [H,\rho] $}

The standard formal solution of this equation is:

{$ (2) \qquad\qquad \rho(t) = e^{iHt/\hbar} \rho_0 e^{-iHt/\hbar} $}

This can be easily checked by calculating the time derivative of both members:

{$ (3) \qquad\qquad \frac {d \rho} {dt} = \frac i \hbar H \rho - \rho \frac i\hbar H$}

< Appendices | Index | The interaction representation >