Answer Happy

need all parts with clear explanation not copy from previous answer allowed
(a) A spin-1/2 particle in the state IS. +) goes through a Stern-Gerlach analyzer having orientation in = cos € 2-sinf (see Fig. 27). What is the probability of finding the outgoing particle in the state [S₁, +)? (b) Now consider a Stern-Gerlach device of variable orientation (Fig. 28). More specifically, assume that it can have the three different directions ₁ = = cos 0 2 - sin 08 ₂ = cos (0+) 2 - sin (0+) & 3 = cos (+) 2 - sin (0 + 7) Fig. 27 Tilted Stern-Gerlach apparatus. #1 113 Fig. 28 Stern-Gerlach device with variable orientation. sem
Source Fig. 29 A pair of spin-1/2 particles emitted in opposite directions. The arrows in the circles represent the field directions in the Stern-Gerlach analyzers. with equal probability (1/3). If a particle in the state |S₂+) enters the analyzer, what is the probability that it will come out with spin eigenvalue +ħ/2? (c) Calculate the same probability as above but now for a Stern-Gerlach analyzer that can have any orientation with equal probability. (d) A pair of particles is emitted with the particles in opposite directions in a singlet 10 0) state. Each particle goes through a Stern-Gerlach analyzer of the type introduced in (c); see Fig. 29. Calculate the probability of finding the exiting particles with opposite spin eigenvalues.