Relation between Dirac's equation density matrix and current with spin

[forofo]

TL;DR Summary

After computind dirac 1D equation for a free particle particle I get 2 matrixs. From both,them I extract the probablity matrix and the current matrix. I'm asking how to extract the two singles values for the spin up and down from there, those that used in quantum computing, the states .

After computind dirac 1D equation time dependant for a free particle particle I get 2 matrixs. From both,them I extract:
1) the probablity matrix P =ps1 * ps1 + psi2 *psi2
2) the current matrix J = np.conj(psi1)*psi2+np.conj(psi2)*psi1

I think that current is related to electricity, and since we are talking about a single free particle, it must have a relation with the spin drawed in the bloch sphere with the two single values or states, that represent the probaility for spin up or down, So how do I extract these 2 values from this matrix J.

how to extract the spin to this

clik here to see the source code in phyton

 

[azntoon]

I'm not sure if I understand your question correctly, but it seems like you're asking how to extract the spin from the current matrix J. If this is the case, then the answer would depend on how the current matrix J is defined in the code. If it is defined in terms of the probability matrix P, then the spin can be extracted from the probability matrix P using the formula S = P*sign(P).