Problem 30. 1989-Spring-QM-U-3.jpgID:QM-U-653A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrixrepresentations of the spin operators areŜT=ħ 0 12 1 070$,- / [87]Sy2i012/0)=1ŜT: [3]+) + | −)] .√10=The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian forthe particle is H=wS, where w = - -B. At t = 0 the wavefunction of the particleisħ2 01 0-1]1. At t = 0, S₂, is measured. What are the possible results of this measurement,and what is the probability of each being obtained?2. Instead of measuring S₂, at t = 0, it is measured at some later time t. Whatare the possible results of this measurement, and what is the probability of eachbeing, obtained? Is Sz, a constant of the motion?

Answered: Image /qna-images/answer/46d5fb4f-6755-43d8-80df-360434a47f5f.jpg

Problem 30. 1989-Spring-QM-U-3.jpg ID:QM-U-653 A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix representations of the spin operators are ST = 0 [83] 1 0 = ħ 0 - ? 2 i 0 ST 1 |gbo) = √√ [3]+) + | −)]. 10 : = [1 ] The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for the particle is H=wS, where w=-B. At t= 0 the wavefunction of the particle is ħ 1 0 0 -1 1. At t = 0, S₂, is measured. What are the possible results of this measurement, and what is the probability of each being obtained? 2. Instead of measuring Sz, at t = 0, it is measured at some later time t. What are the possible results of this measurement, and what is the probability of each being, obtained? Is Sz, a constant of the motion?

Problem 30. 1989-Spring-QM-U-3.jpg ID:QM-U-653 A spin-1/2 particle's state space has a basis |+), |-). On this basis the matrix representations of the spin operators are ST = 0 [83] 1 0 = ħ 0 - ? 2 i 0 ST 1 |gbo) = √√ [3]+) + | −)]. 10 : = [1 ] The particle is in a uniform magnetic field in the +x-direction, so the Hamiltonian for the particle is H=wS, where w=-B. At t= 0 the wavefunction of the particle is ħ 1 0 0 -1 1. At t = 0, S₂, is measured. What are the possible results of this measurement, and what is the probability of each being obtained? 2. Instead of measuring Sz, at t = 0, it is measured at some later time t. What are the possible results of this measurement, and what is the probability of each being, obtained? Is Sz, a constant of the motion?