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I am studying Spin 1/2 system, the case of 2 electrons in a magnetic field, since we have 2 electrons, we expect that the matrix will be of the size 4x4, which is what I have got.

As I know that I could use the density matrix to calculate the expectation values of any physical quantity such us <S_{z}> , <S_{x}> and <S_{y}> by taking the trace of the product of the density matrix with the one we want to find out.

but the point that disappointed me is that S_{z}operator for example is 2x2 matrix , and the density matrix is 4x4 ! I cant take a product of two matrices !

What is the best way to proceed ?

I am really struggling with this, I hope someone would help ()

Thank you

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# I Density matrix

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