# Calculating Time Evolution of Density Matrix

• dg88

#### dg88

Hi,

I am trying to calculate the time evolution of a density matrix. Like if there is a mixed state with 50% of |x, 0> and 50% of |y, 0>. After time t due to time evolution, the kets become:

|x,t>= e^(-i/h Ht) |x,0> and so on.

Is it ok to use these kets instead of the original ket to calculate the density matrix after time t? Or is there another method to do it?

Hi,

I am trying to calculate the time evolution of a density matrix. Like if there is a mixed state with 50% of |x, 0> and 50% of |y, 0>. After time t due to time evolution, the kets become:

|x,t>= e^(-i/h Ht) |x,0> and so on.

Is it ok to use these kets instead of the original ket to calculate the density matrix after time t? Or is there another method to do it?

Yes, but don't forget to take the Hermitian conjugate:

<x,t| = <x,0| e^(i/h Ht)

So, you see that if you do this the density matrix evolves in time according to the unitary time evolution:

rho(t) = U rho(0) U-dagger

U = e^(-i/hbar H t)