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Quantum Mechanics Operators question

  1. Jul 7, 2010 #1
    1. The problem statement, all variables and given/known data

    The operator Q obeys the commutation relation [Q, H] = EoQ, where Eo is a constant with units of energy. Show that if ψ(x) is a solution of the time-independent Schrodinger equation with energy E, then Qψ(x) is also a solution of the time-independent Schrodinger equation, and determine the energy corresponding to Qψ(x).

    2. Relevant equations

    Commutator calculation and properties

    ? Time-independent Schrodinger equation and solution

    3. The attempt at a solution

    QH-HQ = EoQ

    Q = (QH-HQ)/Eo

    Qψ = QC1eiA1/2x+QC2e-iA1/2x
     
  2. jcsd
  3. Jul 7, 2010 #2

    nicksauce

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    Your approach seems a little strange. ψ satisfies Hψ = Eψ (the time independent Schrodinger equation). Then write an expression for H(Qψ) by using the commutator you are given and the fact that Hψ = Eψ.
     
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