Hello,

I am having problems understanding the definition of the density matrix.

In the Spin Dynamics course we learned, that: rho = |psi><psi|. For a spin 1/2 with the two possible states this can be then [1,0;0,0] or [0,0;0,1]. Since adding/substracting the Identity doesn't change the expectation values or the time evolution, we substract -1 to get the same form as for the Hamiltonians = half the Pauli Matrices. So far so good. The problem comes with a spin 1 particle. Then per definition the states are:

[1,0,0; 0,0,0; 0,0,0]

[0,0,0; 0,1,0; 0,0,0]

[0,0,0; 0,0,0; 0,0,1]

From neither of these do we get easily with adding/substracting the 3x3 identity to the Iz operator [1,0,0; 0,0,0; 0,0,-1].

I am obviously missing something in this logic... can anyone tell me what it is?^^

Cheers, Eni

## Definition of the Density Matrix for higher spins

### Re: Definition of the Density Matrix for higher spins

Actually, you do get the right answer for any spin. The spin-half case was:

(+1/2)*|up><up| + (-1/2)*|down><down|

In the spin-1 case you have:

(+1)*|up><up| + (0)*|middle><middle| + (-1)*|down><down|

so exactly the same process.

(+1/2)*|up><up| + (-1/2)*|down><down|

In the spin-1 case you have:

(+1)*|up><up| + (0)*|middle><middle| + (-1)*|down><down|

so exactly the same process.

### Re: Definition of the Density Matrix for higher spins

Ah thank you, Prof. Kuprov.

I think I was missing the multiplication with the expectation values. It is more clear now.

I think I was missing the multiplication with the expectation values. It is more clear now.