I need some help with this quantum mechanics question. 2.The spin singlet state and the EPR experimentConsider the entangled state of two spin-1/2 particles: |4) = (+)₁|-)2 − |−)₁| +)2)Show that this 2-spin state ) is properly normalized.b) Is this state ) an eigenstate of S₁z (i.e. the operator associated with measuring the z-component of the spin of particle 1 only)? If so, what is the eigenvalue? If not, why not?a)c) Is state ) an eigenstate of the "total z-component of spin operator" S₁z + Szz? If so,what is the eigenvalue? If not, why not?d) Show that this entangled state ) is physically equivalent to the more general state:(+)1n| -)2n − |-)₁n] +)2n), where ñî is a unit vector in an arbitrary direction. Hint: It maybe easier to start with the more general state and work your way backwards to the initial state.This result shows why the two detectors in the EPR experiment record perfect anticorrelations intheir spin measurements, independent of the orientation of their detectors, when both detectorsare aligned along the same direction!e) Given the state ), show that the probability of observer A to measure particle 1 with spinup is 50% for any orientation of observer A's Stern-Gerlach apparatus. Hint: To find thisprobability, sum over the joint probabilities for observer A to measure spin up for particle 1along the chosen direction and observer B to measure any spin orientation for particle 2. Tosimplify the calculation, choose observer B's Stern-Gerlach apparatus to be oriented along the zdirection. You'll have to add the probabilities for the cases where B measures spin up and spindown.

Question

I need some help with this quantum mechanics question. 2.The spin singlet state and the EPR experimentConsider the entangled state of two spin-1/2 particles: |4) = (+)₁|-)2 − |−)₁| +)2)Show that this 2-spin state ) is properly normalized.b) Is this state ) an eigenstate of S₁z (i.e. the operator associated with measuring the z-component of the spin of particle 1 only)? If so, what is the eigenvalue? If not, why not?a)c) Is state ) an eigenstate of the &#34;total z-component of spin operator&#34; S₁z + Szz? If so,what is the eigenvalue? If not, why not?d) Show that this entangled state ) is physically equivalent to the more general state:(+)1n| -)2n − |-)₁n] +)2n), where ñî is a unit vector in an arbitrary direction. Hint: It maybe easier to start with the more general state and work your way backwards to the initial state.This result shows why the two detectors in the EPR experiment record perfect anticorrelations intheir spin measurements, independent of the orientation of their detectors, when both detectorsare aligned along the same direction!e) Given the state ), show that the probability of observer A to measure particle 1 with spinup is 50% for any orientation of observer A's Stern-Gerlach apparatus. Hint: To find thisprobability, sum over the joint probabilities for observer A to measure spin up for particle 1along the chosen direction and observer B to measure any spin orientation for particle 2. Tosimplify the calculation, choose observer B's Stern-Gerlach apparatus to be oriented along the zdirection. You'll have to add the probabilities for the cases where B measures spin up and spindown.

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