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Homework Help: Quantum Physics - hermitian and linear operators

  1. Dec 2, 2012 #1

    1. Prove that operators i(d/dx) and d^2/dx^2 are Hermitian.

    2. Operators A and B are defined by:



    Check if they are linear.

    The attempt at a solution

    I noted the proof of the momentum operator '-ih/dx' being hermitian, should I just multiply all the terms involved in it by '-1/h'? I do not really know what should I do in the second exercise.
  2. jcsd
  3. Dec 2, 2012 #2


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    -ihbar d/dx is hermitean. You say you have the proof. Now dropping hbar which is a real (as opposed to an imaginary) constant, does it change the hermitean character or not ?

    As for the second derivative operator, assuming wavefunctions dropping to 0 when going to infinity, can you show that it's hermitean by maneuvering the integrals ?

    Consider the definition of linearity. It's not more complicated than that.
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