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Homework Help: Quantum linear operators

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    Just starting third level Uni. stuff & am faced with linear operators from Quantum Mechanics & need a little help.
    OK, an operator, Ô, is said to be linear if it satisfies the equation
    Ô(α f1 + β f2) = α(Ô f1) + β(Ô f2)

    but I have an equation I can't wrap my head around, maybe just rusty, a hint would be nice, though.

    2. Relevant equations
    Ô1 = d/dx;
    Ô2 =3 d/dx +3x^2;

    Find the new functions obtained by acting with each of these operators on
    (a) g(x, t) =3 d/dx +3x^2
    (b) h(x, t)=α sin(kx − ωt).

    3. The attempt at a solution
    Ô1 g(x,t) = 6xt^3
    But not sure about how to get
    Ô2 g(x,t) =

    how to get this middle bit, please . . . . .

    Answer is 18xt^3 + 9x^4 t^3
  2. jcsd
  3. Jan 30, 2013 #2


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    Science Advisor
    Homework Helper

    You realize there's no 't' dependence in g(x,t), so that the outcome must be independent of t, right ? Actually the way you wrote it, g(x,t) is Ô2, not a wavefunction, but also an operator.
  4. Jan 30, 2013 #3
    I went back to the question, scanned the problem in & looking again showed a huge error in seeing things.
    What a twit.
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