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Eigenstates and eigenvalues

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data

    I have the hamiltonian :

    H=C(|2><1|+|1><2|)

    where :
    C=costant
    |1> and |2> are eigenstates of an osservable A.

    what are the eigenstate and eigenvalues of the hamiltonian?
    what is the probability that the system is in the state |2>?

    3. The attempt at a solution

    eigenstates :

    |1>+|2>, |1> - |2>, -|1> - |2>,-|1>+|2>

    eigenvalues (respectively):

    C , -C, C, -C

    ad es:

    H(|1>+|2>)=(C(|2><1|+|1><2|)) (|1>+|2>)=C |2> <1|1> + C |2><1|2> + C |1> <2|1> + C |1> <2|2>= C |2> <1|1> + C |1> <2|2>= C (|1>+|2>)
     
  2. jcsd
  3. Dec 8, 2008 #2

    Redbelly98

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    A 2x2 matrix should only have 2 eigenstates.
     
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