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Homework Help: Please help.[quantum]

  1. Nov 19, 2007 #1
    Please urgent help.[quantum]

    I have a homework I have tried a lot of thinks but I couldnot manage to solve.

    problem: for two particle j1 = 2 ; j2 = 1 and the condition is m=m1 + m2 = 2.
    by using Clebsch Gordan coefficients for the possible states !22> and !32>, create a matrix which will be a 2x2 matix lest say U and create j square for the system.
    find the matrix product U(transpose).j(square).U.
    I know that this pruduct will be the identity matris I if you take the h(bar) as 1
    I have created the matrix U that is -squareroot(1/3) squareroot(2/3)

    squareroot(2/3) squareroot(1/3)

    but I have problem with the j(square)

    I know the j(square)= j1(square) + j2(square) + [(j1-.j2+) + (j1-.j2+)] + 2j1z.j2z

    here j1- and j2- are lowering and j1+ and j2+ are rising optrs.

    please someone help me with the building of j(square) matris. I really have done whatever I can do.
    Last edited: Nov 19, 2007
  2. jcsd
  3. Nov 19, 2007 #2
    for example for j1(square) matrix elements are j1(j1+1) that is 6 in the diagonal of 2x2 matris and off diagonal elements are zero.
  4. Nov 20, 2007 #3
    please someone help me. I really worked on this problem.
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