- #1
Guilherme Vieira
- 3
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Hello, I'm trying to understand how to calculate de probability of finding a system in a specific eigenstate using the density operator. In the book of Balian, Haar, Gregg I've found a good definition of it being the expectation value of the projector Pr in the orientation of the eingenstate.
P(a) = tr(D.Pra)
The problem is, since I have then a product between de density matrix tr(D.Pra), Pra would have to be a matrix of the same rank of D, write ? To calculate then the tr. What is the right way to construct the projection ?
Transform the state, a vector, into a matrix ? Beeing a matrix with just one element in the main diagonal for each of the a directions relative to each eingenstate ?
I'm a new member, so I'm not used to ask questions online. Thank you.
P(a) = tr(D.Pra)
The problem is, since I have then a product between de density matrix tr(D.Pra), Pra would have to be a matrix of the same rank of D, write ? To calculate then the tr. What is the right way to construct the projection ?
Transform the state, a vector, into a matrix ? Beeing a matrix with just one element in the main diagonal for each of the a directions relative to each eingenstate ?
I'm a new member, so I'm not used to ask questions online. Thank you.