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About wavefunctions of Hydrogen atom

  1. Mar 30, 2006 #1
    Every one knows that wavefunctions are generally complex functions described by three quantum numbers n, l and m, and the number m is included in the form exp(i*m*fai). But here in the following webpage they are all real functions, I'm confused:confused: . Can anyone help me?

    Thank u in advance!
  2. jcsd
  3. Mar 30, 2006 #2


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    Staff: Mentor

    Uh, what web page? :confused:
  4. Mar 30, 2006 #3
  5. Mar 30, 2006 #4


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    Staff: Mentor

    That page makes a mistake in listing (for example) the [itex]2p_x[/itex] and [itex]2p_y[/itex] wave functions as having m = 1 and -1. They are actually linear combinations of the functions with m = 1 and -1. Recall that

    [tex]\cos \phi = \frac{e^{i \phi} + e^{-i \phi}}{2}[/tex]

    [tex]\sin \phi = \frac{e^{i \phi} - e^{-i \phi}}{2i}[/tex]

    If you measure [itex]L_z[/itex] for either of these functions, you get [itex]+ \hbar[/itex] half the time, and [itex]- \hbar[/itex] half the time, randomly.

    The [itex]p_x[/itex] and [itex]p_y[/itex] functions are convenient for some purposes because they have lobes along the x and y axes, just like the [itex]p_z[/itex] (m = 0) function has lobes along the z axis.
  6. Mar 30, 2006 #5


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    Wave functions can be real; typically this is the case for bound states. (Strictly speaking this holds for the radial function.) Think about harmonic oscillator wave functions -- they are real. Pretty standard stuff.
    Reilly Atkinson
  7. Mar 30, 2006 #6

    Hans de Vries

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    In Cartesean coordinates it's clearer:

    [tex] p_z\ \ \propto\ \ \cos{\theta}\ =\ \frac{z}{r}[/tex]

    [tex] p_x\ \ \propto\ \ \sin{\theta}\cos{\phi}\ =\ \frac{x}{r}[/tex]

    [tex] p_y\ \ \propto\ \ \sin{\theta}\sin{\phi}\ =\ \frac{y}{r}[/tex]

    They are all the same.

    Regards, Hans
    Last edited: Mar 30, 2006
  8. Mar 30, 2006 #7
    Yes, I agree with your opinion very much!:approve:

    There must be something wrong.

    Thanks a lot:smile:
  9. Mar 30, 2006 #8
    I don't mean all wavefunctions must be complex.

    But thank u all the same!
  10. Mar 31, 2006 #9
    en, it's clearer.
  11. Mar 31, 2006 #10
    I don't know how to type mathematical equations here, it's too inconvenient.:cry:

    How do you do that?
  12. Mar 31, 2006 #11


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  13. Mar 31, 2006 #12
    It seems that all the equations are copied piece by piece, then typying equations will be too laborious a task:surprised

    Is there a shortcut?
  14. Mar 31, 2006 #13
    Not really. But LaTex is easy once you get past the initial shock.
  15. Mar 31, 2006 #14
    I think a compact software like mathtype will help greatly.
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