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Superposition Equation solution

  1. Apr 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi everyone,
    This is my first time posting, and I really need some help. I'm doing a project on Schrodinger's cat, concentrating on superposition and the linearity of operators.
    I have this equation: |\psi\rangle = {3\over 5} i |A\rangle + {4\over 5} |B\rangle
    but I don't know what amounts to plug in for A and B, as well as what amount the imaginary number represents, if anything.



    2. Relevant equations
    |\psi\rangle = {3\over 5} i |A\rangle + {4\over 5} |B\rangle

    3. The attempt at a solution
    I think I understand what the equation is saying, that if a particle can be at A and B, it can also be 3/5i in position A and 4/5 in position B. But beyond that, I don't know what step to take next.

    Any input would be extremely helpful
    thanks!
     
  2. jcsd
  3. Apr 29, 2008 #2
    Hi asechman,
    |A> and |B> are abstract representations of quantum states. You don't plug in anything for A and B. They are just labels used to distinguish the states.

    Let's say you're making a measurement, and |A> and |B> represent two possible states resulting from that measurement. Then the formula

    [tex]
    |\psi\rangle = N_A |A\rangle + N_B |B\rangle
    [/tex]

    means that the probability of finding the system in state A is

    [tex]P_A = |N_A|^2 = {N_A}^*N_A[/tex]

    and the probability for finding the system in the other state is

    [tex]P_B = |N_B|^2 = {N_B}^*N_B[/tex]
     
    Last edited: Apr 29, 2008
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