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Need help with Schrödinger and some integration!

  1. Nov 30, 2014 #1
    • Moved here from non-homework forum, therefore template is missing
    My wave function:
    ##\psi_2=N_2 (4y^2-1) e^{-y^2/2}.##
    Definition of some parts in the wavefunction ##y=x/a##, ##a= \left( \frac{\hbar}{mk} \right)##, ##N_2 = \sqrt{\frac{1}{8a\sqrt{\pi}}}## and x has an arrange from ##\pm 20\cdot 10^{-12}##.
    Here is my integral:
    ##<x^2> = \int\limits_{-\infty}^{\infty}\psi_2^*x^2\psi_2dx.##
    It should integrate it directly or with Hermite polynomials: http://en.wikipedia.org/wiki/Hermite_polynomials
    I don't know how to do that. And I does ##\psi_2^*## mean it is conjugated? Really need some help here. I don't know how to start. If someone could help me, it would be great!
    Thank you very much in advance!
     
    Last edited: Nov 30, 2014
  2. jcsd
  3. Nov 30, 2014 #2

    Matterwave

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    please use two $-signs for latex wrappers, and two #-signs for in-line latex.
     
  4. Nov 30, 2014 #3

    jtbell

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    Staff: Mentor

    What, specifically, do you not know how to do? What to substitute for ##\psi_2##? What to substitute for ##\psi^*_2##? How to evaluate the resulting integral?

    Yes, ##\psi^*_2## is the complex conjugate of ##\psi_2##.
     
  5. Dec 1, 2014 #4

    I don't what I should substitute ##\psi^*_2## with. ##\psi_2## would I substitute with the ##\psi_2## function and Integrate for the limits ##\pm \infty## (of course ##dx##). The same would I do with ##x^2##. I would do the same with ##\psi^*_2## and at the end I would * them together. Is it correct or totally wrong?

    But still I don't know how to substitue ##\psi^*_2##.
     
  6. Dec 1, 2014 #5

    DrClaude

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    Staff: Mentor

    That doesn't work: the integral of a product is not equal to the product of integrals. Try it for yourself: is ##\int x^2 dx = (\int x dx)^2## true?

    What is the complex conjugate of ##\psi^*_2##?
     
  7. Dec 1, 2014 #6
    I don't know what the complex conjugate og ##\psi^*_2## is. How to figure it out? I know what ##\psi_2## is.

    When I know what ##\psi_2^*## is, I should just put it in the formular, insert the ##\psi_2## in the formular, find the product and then integrate, am I right?

    But what is the complex conjugate of ##\psi_2##? How to figure it out? What is ##\psi_2^*## equal with when I know ##\psi_2##? But in this case ... is ##\psi^*_2 =\psi^2##?
     
    Last edited: Dec 1, 2014
  8. Dec 1, 2014 #7

    DrClaude

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    Generally speaking, how does one do complex conjugation?
     
  9. Dec 1, 2014 #8

    jtbell

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    No, but if you make a small change to the right side it will be correct!
     
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