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The Heisenberg Representation

November 25, 2008

\displaystyle\left|\psi_S(t)\right>=U(t,t_0)\left|\psi_S(t_0)\right>

\displaystyle\left|\psi_H\right>=U^{\dagger} (t,t_0)\left|\psi_S(t)\right>=\left|\psi_S(t_0)\right>

An observable A_S in the Schrödinger representation transforms into:

\displaystyle A_H=U^{\dagger}(t,t_0)A_SU(t,t_0)

In general A_H is not stationary even when A_S doesn’t depend explicilty upon time.

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