Question

3. (6 points) Measurements on a two-particle state Consider the state for a system of two spin-1/2 particles, (2]+).I+)2 +1-)
(a) Show that this state is normalized. (b) What is the probability of measuring S: (the z-component of spin for particle 1)
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Answer #1

ANS: The state for a system of two spin-1/2 particles. 1 + >,! + + 1 -/+ > -|-71-72) Narmalisation condition ; <41 h 12 <+ lq<44 > 1 state Ý Normalized. Eigenstate coresponding to valve seat at ý 1+7 Probability amplitude of getting out the < +1 > (xPro bability of getting samt + x3y2 keltal . Æ Eto: ofter the measurment state & System y say 10> ( + lø>) 1+2 10> - to [2 1Probability & getting go + 13 1 © Probability of getting sett K-14>12 < 414 > &+?-171-37 +(2+12+) 1-3 ] e re <al- [(2-16-1) -ý zero Probabity į posible. state No such : groba bity g measurny sa and ý also the /> state Zero in they are then Commutershults go first eporating si on lu> - 1+2 + 12 -1 -2 8 to) Šo (21+%, 17% +1-703 2-12-1- (2+16-17 +3 +(2+*+1) 1+ 3 ) 8/47 (² +Summary : - To find probability in a given states ý find by taking inner Products of normalised Psi with the given a state an

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