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Homework Help: Quantum mechanics question

  1. Jun 2, 2010 #1
    1. The problem statement, all variables and given/known data
    A system in a state with L=1, S=1, J=2, Mj=2 and odd parity decay in a particle [tex]\Delta^-[/tex] (even parity and spin 1/2) and in a proton (even parity).

    1) Find the possible momenta of S and L of the final system
    2) Find the most general final system
    3) Find the angular distribution of probability to find both particles with spin parallel to z axis.

    3. The attempt at a solution
    1)
    Final S=0,1
    Final L=2 (S=0) or L=1,2,3(S=1)
    but L=1 and L=3 is not admissible due to the parity conservation

    So there is only: S=0, L=2
    or S=1, L=2

    2)The two final states are
    [tex]|2022>=|2020>[/tex]
    [tex]|2122>=\frac{\sqrt{2}|2120>-|2111>}{\sqrt{3}}[/tex]

    where the notation is: [tex]|L,S,J,Mj>=|L,S,m_L, m_S>[/tex]

    I don't know in which of this two states the particle will decay, so I have to consider the general state:
    [tex]\alpha|2020>+\beta\frac{\sqrt{2}|2120>-|2111>}{\sqrt{3}}[/tex]
    with [tex]|\alpha|^2+|\beta|^2=1[/tex]

    3) The probability is the [tex]|\frac{\beta}{3}Y_2^2|^2[/tex]
    But I don't know how to find alpha and beta
     
    Last edited: Jun 2, 2010
  2. jcsd
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