As we mentioned before, a density matrix with weight w for an ensemble is in a from:

For any Operator Q, the expectation value is:

for a random polarization state:

where I is identity matrix. any density matrix can be expressed by the polarization vector π.

where λ is a normalization factor and σ is the Pauli’s matrix.

from this post, we knew that the out-spin and in-spin is related by the “scattering amplitude matrix” F.

the in-density matrix for an ensemble is:

thus, the out-density matrix is:

which is just the usual transformation rule for density matrix or a general tensor.

For a single particle, we have :

For an ensemble, we have:

### Like this:

Like Loading...

## Leave a Reply