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Homework Help: Eigenfunction concept

  1. Sep 28, 2008 #1
    I am a seond year Quantum Chemistry student. I am having a hard time understanding these concepts. I was wondering I can get help in this concept.

    How can it be demonstrate mathematically in the Hamiltonian operator that the function
    φ(x) = A sin(2x) + B cos(2x)

    is an eigenfunction of the Hamiltonian operator:
    H=-h^2 d^2
    2m dx^2

    What is the eigenvalue equal to?
  2. jcsd
  3. Sep 28, 2008 #2


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    Homework Helper

    Yikes. That is very difficult to read. You should try and learn some TeX. It is good for the soul, and for the typesetting. for example:


    I believe that If you click on the above equation it will show you the TeX source that I used to write the equation in such a pretty manner.

    Anyways. In order to do what you want you need to take the derivative of
    A\sin(2 x)+B\cos(2 x)

    what do you get?

    Then multiply by

    That is what the symbols on the right hand side of the equation for [itex]H[/itex] are instructing you to do.

    What is the end result?

    Is it proportional to
    A\sin(2 x)+B\cos(2 x)

    What is the proportionality constant?
  4. Sep 29, 2008 #3
    In case you are not aware of eigenfunctions:
    http://mathworld.wolfram.com/Eigenvalue.html" [Broken]
    Last edited by a moderator: May 3, 2017
  5. Sep 30, 2008 #4
    I found the two derivatives and I found that the function φ(x) = A sin(2x) + B cos(2x)
    is an eigenfunction of the Hamiltonian operator:

    H=-h2 d2
    2m dx2

    and the proportionality constant is

    Can someone confirm with me if this is right or what did I do wrong?

    Thanks so much for all the help.
  6. Oct 1, 2008 #5


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    Homework Helper
    Gold Member

    Yes, you have the correct eigenvalue (proportionality constant).
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