5. Spin-3/2 system (25 points) There are four possible states in a spin 3/2 particle. We may choose these states as the

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5 Spin 3 2 System 25 Points There Are Four Possible States In A Spin 3 2 Particle We May Choose These States As The 1 (78.37 KiB) Viewed 94 times

5. Spin-3/2 system (25 points) There are four possible states in a spin 3/2 particle. We may choose these states as the eigenstates of Ŝ2: Ŝ2|m) mm). where m = 3/2, 1/2, -1/2, and -3/2 (set ħ = 1). We may also define the raising/lowering operators Š= $c = iŜy, which have the following properties: 3 15 4 0. $+/m) - m(m£1)|m£1), and S+1) +1Sul ŜI – 3 (a) (10 points) Find the matrices form for the operators Ŝt, Ŝa, Ŝy, and Ŝ, in these bases (and the rest part of this problem) 1 1 3-0--0--- 3 = = 0 0 1 0 and 0 0 0 1 (b) (8 points) What are the eigenvalues for Ŝ? Find the eigenvector corresponding to the maxima eigenvalue of Sq. (c) (7 points) You prepare a state [) which is the eigenstate of Ŝe with the maxima eigenvalue. Now you measure Şu, what values you will obtain? with what probability for each value you measure? What is the expectation value (4|9z|v)?