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-)[+)2-1-)1-)2).

Answer 1

ANS: The state for a system of two spin-1/2 particles. 1 + >,! + + 1 -/+ > -|-71-72) Narmalisation condition ; <41 h 12 <+ lq<+ lg +<+k<-12-4-62-14) bakin inner product d iv> and <yol --@ <\/p>sto [+le <+1)(1+2,1+r) + (x+h <-10) (-3314x) + (<-<-1)(-30-2)] to [H2+ 12 (x +1+) + <+126-1-4]itz +3+13 [<=->a) |->] 3+1+3=1 ; {+-% -1 +/+) :1 ; 3 1 -) : 1 -ţ [4 € +1+3 + +1+2 +601-172] [ 4+1+1]

<44 > 1 state Ý Normalized. Eigenstate coresponding to valve seat at ý 1+7 Probability amplitude of getting out the < +1 > (x+12-17 1 + 8 + (*+*+171 +36] 27. ta (270-6] k +1+3 To

Pro bability of getting samt + x3y2 keltal . Æ Eto: ofter the measurment state & System 'y say 10> ( + lø>) 1+2 10> - to [2 17 21 +] Now govoba bity of measuring sage = + ħ lo 5+19 > 1 1 <010>1 Finding 2016> a to [uçte +1+%21+] - ] [4+1+>] and 5tlo) da La $ +ILI+al+)] ho

Probability & getting go + 13 1 © Probability of getting sett K-14>12 < 414 > &+?-171-37 +(2+12+) 1-3 ] e re <al- [(2-16-1) - bo (0+1+] +0. qoy oh boility and getting sites ) state ofter measurment į say hey Iko>. (8-14>) 1-74.

ý zero Probabity į posible. state No such : groba bity g measurny sa and ý also the /> state Zero in they are then Commuters Sq? € If she and observaoubles. compatible to be said .0 2 به 4 ( - يه دو) 0: < بود و در حد شيو 40 < هل ( ج - ش شيري) 0: < و و و. < دا و ھو 0 - <پا شود و با تو شد ý true or not o cavation this Find let - - - + + + ا ء شود ا -><- 1 ( - ) + + +۱ سود کی Ctry

hults 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 + 1 - 1) = -$+(1-31-2)] -1-2 -> [to (2¢-+(1+), 1 + x) +5 -0 (1->11+ 2) -5-1 (1-2, 1-2)] - I+>) (241-0) (1-2) (010-1) + now operating st on this new state k> 2421 2 4 2 + 2) (%-> *-1 & 4 - 9 +74+1 2. (11,8 similary, s > 20.

Summary : - To find probability in a given states ý find by taking inner Products of normalised Psi with the given a state and then savare that And for Compability use communication relations . IP commotetor bracket ý zero then both s would Commute.