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

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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 .

Main Question or Discussion Point

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
jp.JPG

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.
jpdibu.JPG
how to extract the spin to this
spindibu.JPG


clik here to see the source code in phyton
 

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