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Momentum Operator

  1. Mar 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi, my task is to show that the momentum operator is hermitian.

    I found a link, which shows how to solve the problem:

    http://www.colby.edu/chemistry/PChem/notes/MomentumHermitian.pdf

    But there are two steps that I don't understand:

    1. Why does the wave function approach zero for long distances (for a confined particle)? Can someone explain me this?

    2. I don't understand the last step. I got xMHR6K1.png

    And now i don't know how to use the last equation on the paper to show that it is the same.

    Can someone help me?

    2. Relevant equations
    See above

    3. The attempt at a solution
    See above
     
  2. jcsd
  3. Mar 10, 2016 #2

    vela

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    Do you know the definition of hermitian?
     
  4. Mar 10, 2016 #3
    I know what a hermitian matrix is. But here I'm not sure. I guess that the operator is the same as the complex conjugate of the operator?
     
  5. Mar 10, 2016 #4

    vela

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    You should start there then. There's no need to guess. The definition should be explained on your textbook or notes. You want to figure out specifically what it means when you say an operator is the same as its complex conjugate. It's probably explained in terms of inner products.
     
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