The density matrix for a pure system

Consider a system characterized by agiven Hamiltonian operator., an orthonormal basis (/) (also denoted n ) that spans the corresponding Hilbert space and a time dependent wavefunction h (i)—a normalized solution of the Schrodinger equation. The latter may be represented in terms of the basis ftmctions as 

The normalization of T (Z) implies that I C p = 1. When the state of the system 

Consider also a dynamical variable A that is represented by an operator A. Its expectation value at time t is given by 

The coefficients p i in (10.2) define the matrix elements of the density operator p in the given basis. For a pure state p can be written explicitly as 

The time evolution ofthe density operator can be found from the time evolution of F(Z) and the definition (10.3)  

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