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Help regarding normalization of wave functions

  1. Jan 28, 2010 #1
    Hi, i need some help regarding normalization of a wave function, i feel it is a very simple problem, but i am having a hard time figuring it out. I would really appreciate it if anybody could help me out a bit regarding this.

    I need to normalize the following wavefunctions by figuring out the constant B.

    (1) ψ(x) = Bexp(ikx) where ψ(x) is non‐zero between x=0 and x=L ;
    (2) ψ(x) = Bexp(−kx) where ψ(x) is non‐zero between x=0 and x=∞

    Thanks a lot in advance.
     
  2. jcsd
  3. Jan 28, 2010 #2

    jtbell

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    Staff: Mentor

    Do you know what it means for a function to be normalized? What equation or property does a normalized function have to satisfy?
     
  4. Jan 28, 2010 #3
    |ψ(x)|² = 1

    So legend square both sides, set |ψ(x)|² equal to one. then solve for B
     
  5. Jan 28, 2010 #4
    Thanks a lot dacruick.

    @jtbell... actually i have some vague idea, i am still in the process of coming to terms with quantum mechanics (i don't have a physics background :-( )
     
  6. Jan 28, 2010 #5

    Avodyne

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    Science Advisor

    Wrong.
     
  7. Jan 28, 2010 #6

    jtbell

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    Staff: Mentor

    No, you also have to integrate. In general:

    [tex]\int^{+\infty}_{-\infty}{|\psi(x)|^2 dx}
    = \int^{+\infty}_{-\infty}{\psi^*(x)\psi(x) dx} = 1[/tex]

    In this case, one actually has to integrate only over the region where [itex]\psi(x)[/itex] is non-zero.
     
  8. Jan 29, 2010 #7
    If [tex] \psi(x)[/tex] is a period wave with period L or it is in a box

    [tex]\int^{+L}_{0}{|\psi(x)|^2 dx}
    = \int^{+L}_{0}{\psi^*(x)\psi(x) dx} = 1
    [/tex]
     
  9. Jan 29, 2010 #8
    Thanks a lot for your answers. I have one doubt.

    How do i go about the second function i.e Bexp(−kx)? Do i replace "-k" by "i²k" and proceed?
     
  10. Jan 29, 2010 #9
    The wave function is real so [tex]\psi=\psi^*=Be^{-kx}[/tex]. Just integrate as it is and you'll be fine. (Replacing [tex]-k\to i^2k[/tex] will also give the correct answer because it actually does nothing. You don't have to do that.)
     
  11. Jan 31, 2010 #10
    Thanks a lot to all of you guys for your help. So i solved them and got the following results. Could anyone please let me know if they are correct?
    For number 1 : B = 1/(√L)
    For number 2 : B = √(2k)
     
  12. Jan 31, 2010 #11
    Yes, they are correct.
     
  13. Jan 31, 2010 #12
    Thanks a lot
     
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