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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 √34 14) = = | +) + i 1-) 5 34 a) [1] 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? b) [1] If instead, the initial beam is passed through an x-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sx, and with what probabilities? c) [2] 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?

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 √34 14) = = | +) + i 1-) 5 34 a) [1] 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? b) [1] If instead, the initial beam is passed through an x-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sx, and with what probabilities? c) [2] 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?

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1. [7] Practice with state vectors 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: 14) = 3 34 | +) +i5|-) 34 a) [1] 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? b) [1] If instead, the initial beam is passed through an x-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sx, and with what probabilities? c) [2] 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?
Transcribed Image Text:1. [7] Practice with state vectors 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: 14) = 3 34 | +) +i5|-) 34 a) [1] 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? b) [1] If instead, the initial beam is passed through an x-oriented Stern-Gerlach apparatus, what are the possible results of the measurement of Sx, and with what probabilities? c) [2] 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?
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