Akash posted an Question
October 21, 2021 • 18:12 pm 30 points
  • Physical Sciences

Q6. (a) in a system consisting of two spin particles labeled i and 2, let s= and s= denote the corresponding spin operators. here d=lo,.0,a.) and ,,,. are the t

Q6. (A) In a system consisting of two spin particles labeled I and 2, let S= and s= denote the corresponding spin operators. Here d=lo,.0,a.) and ,,,. are the three Pauli matrices. In the standard basis the matrices for the operators S's and S's\ are respectively, (0 10 0 0-i0 0) 0 00-i,0 0 -i th0 0i 0hO 0 -i 0 4 0-i 0 04 0i0 00 i00 0 (d 0 0 0 |n|io o o 4 0 00-i| 4 0 0 0 1 i0 0 0 o 0i 0 o o1 0 H.No. 40-D, Ground Floor, Jia Sarai, Near IIT, Hauz Khas, New Delhi-1 10016 1C10

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    Anshum Sharma

    Here outer product is taken because Sx(1),Sy(2) belongs to different Hilbert space that's why for finding the product of Sx(1) and Sy(2) they did outer product. Here outer product means Sx(1) is the written in complex conjugate form and Sx(2) is written in normal form. if Sx(1) multiple with Sy(1) then you have to do inner product. Now do the outer product of the matrix where the element of 1st matrix is multiplied by the elements of 2nd matrix and written in row and column. see the attached image


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