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The time evolution of states a quantum system is given by the time dependent Schrodinger equation. Besides this framework, called the Schr\"{o}dinger picture, other scheme are possible. In the Heisenberg picture, defined here, the observable evolve according to the equation \[\dd[X]{t} =\frac{1}{i\hbar}[F, H] \]This equation corresponds to the classical equation of motion in the Poisson bracket formalism.

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The time evolution of a general quantum system is reviewed in an abstract setting. The eigen states of energy are seen to have all properties that make them qualify for being called stationary states.The stationary states have the property that all observable quantities remain constant in time.

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A scheme to solve the time dependent Schr\"{o}dinger equation \begin{equation} \label{eq01} i\hbar \dd{t}\ket{\psi} = \hat{H} \ket{\psi} \end{equation} is described. The final solution will be presented in the form, see \eqref{eq14} \begin{equation} \ket{\psi t} = U(t, t_0) \ket{\psi t_0} \label{eq16} \end{equation}where
\begin{equation}\label{EQ16A} U(t, t_0) \ket{\psi t_0} = \exp\Big(\frac{-i H(t-t_0)}{\hbar}\Big)\end{equation}

What coordinates, microscopic or macroscopic, are used in statistical systems?  How are the macroscopic variables are related.

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The question of simultaneous measurement of two dynamical variables is analysed. Starting from the postulates it is argued that two variables can be measured simultaneously if and only of they commute. This result generalizes to simultaneous measurement of several dynamical variables.