# ps9 - Harvard University Physics 143b Quantum Mechanics II...

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Unformatted text preview: Harvard University Physics 143b: Quantum Mechanics II Problem Set 9 due Friday December 3 1. A pair of electrons are placed in the state | t i = 1 √ 2 ( | z, + i| z,-i + | z,-i| z, + i ) Implicitly, the first ket refers of the first electron, and the second to the second electron. So the ordering of the kets is significant and should be carefully preserved in your computations. Also note that this state is not rotationally invariant. (a) The spin of the first electron is measured along the direction n = (sin θ, , cos θ ). What is the probability that a value + is obtained ? Here it will be useful to rewrite | t i in the | n , ±i basis. (b) If the measurement above yields +, what is subsequently the state of the second electron ? You can leave your answer in the | n , ±i basis. (c) Finally, the spin of the second electron is measured along the z direction. What is the probability that a value + is obtained? Here it will be useful to rewrite the answer to (b) in the | z, ±i basis.basis....
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ps9 - Harvard University Physics 143b Quantum Mechanics II...

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