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You may use either the ket notation or the column vector (matrix) notation to do this problem. A beam of spin-1/2 particles is prepared in the initial state: 5 = √3/34 | +) + ²√ √/341 14) = 1-) a) The beam is passed through a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of the spin component Sz, and with what probabilities?

You may use either the ket notation or the column vector (matrix) notation to do this problem. A beam of spin-1/2 particles is prepared in the initial state: 5 = √3/34 | +) + ²√ √/341 14) = 1-) a) The beam is passed through a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of the spin component Sz, and with what probabilities?

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You may use either the ket notation or the column vector (matrix) notation to do this problem. A beam of spin-1/2 particles is prepared in the initial state: 3 14) √34 - | +) +i4|-) a) The beam is passed through a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of the spin component S₂, and with what probabilities? c) If instead, the initial beam is passed through a y-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sy, and with what probabilities? d) After the beam passes through the y-oriented Stern-Gerlach, the component with spin up along the y-direction is directed to a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of Sz, and with what probabilities? e) Draw separate cartoon diagrams for parts c), d), and a) of this problem. Start off with 100 particles, so that the numbers of particles in the final states represent probabilities as percentages. (In other words, if 37% of the initial particles end up going in a certain direction, label that output with 37 particles.) Explain briefly why you get more up-z particles at the end of part d) than do at the end of part a). you
Transcribed Image Text:You may use either the ket notation or the column vector (matrix) notation to do this problem. A beam of spin-1/2 particles is prepared in the initial state: 3 14) √34 - | +) +i4|-) a) The beam is passed through a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of the spin component S₂, and with what probabilities? c) If instead, the initial beam is passed through a y-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sy, and with what probabilities? d) After the beam passes through the y-oriented Stern-Gerlach, the component with spin up along the y-direction is directed to a z-oriented Stern-Gerlach apparatus. What are the possible results of the measurement of Sz, and with what probabilities? e) Draw separate cartoon diagrams for parts c), d), and a) of this problem. Start off with 100 particles, so that the numbers of particles in the final states represent probabilities as percentages. (In other words, if 37% of the initial particles end up going in a certain direction, label that output with 37 particles.) Explain briefly why you get more up-z particles at the end of part d) than do at the end of part a). you
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