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Homework Help: Wave Function

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data

    One wave function of H like atom is [tex]\psi=\frac{\sqrt{2}}{81\sqrt{\pi}a_{0}^{3/2}}(6-\frac{r}{a_{0}})\frac{r}{a_{0}}(e^{\frac{-r}{3a_{0}}})cos \theta[/tex]

    How many nodal surfaces are there?
    1)1
    2)2
    3)3
    4)none of these

    3. The attempt at a solution
    Its an objective question which I need to answer in less than a minute. Is it possible to do so?

    The next thing that I assume i that the wave function is given in polar coordinate form, isn't it?? [tex]\psi=f(r,\theta, \phi)[/tex]???
    phi is absent what does it mean? I guess it means that its the p - orbital. then the anwer must be 2. Am I right????

    Last but not the least. I am keen upon seeing the 3D picture this wave function generates. I have MATLAB but I dont know how to code in polar coordinate and all. Will somebody code this wave function for me which is compatible with MATLAB 2008?? Please. I shall be very grateful.
    Thanks a lot.
     
  2. jcsd
  3. Dec 3, 2008 #2
    Isn't the number of nodal surfaces equal to the quantum number of your wave function?
     
  4. Dec 3, 2008 #3
    Thanks a lot but I know that already. Is it of any help with this particular problem?
    And sir, can you please tell me how can I plot equations such as this one and like
    x2+y2+z2=1 with MATLAB?
     
  5. Dec 3, 2008 #4
    Your given the wave function. The wave functions for the hydrogen atom are constructed from two separate functions, the spherical harmonic wave functions, [tex] Y^{m}_{l}\left(\theta,\phi\right) [/tex], and the radial wave functions, [tex] R_{nl}\left(r\right) [/tex]:

    [tex] \Psi_{nlm}\left(r,\theta,\phi\right) = R_{nl}\left(r\right)Y^{m}_{l}\left(\theta,\phi\right) [/tex]

    You really only need to look at the radial wave equation, since by definition it has a term [tex] e^{-r/na} [/tex], where n is the quantum number. So, this is easily determined by your given function.

    I am pretty certain that n,l,m = 3,1,0 for your given wave function. Here's an applet to check out the probability density:

    http://www.phy.davidson.edu/StuHome/cabell_f/Density.html
     
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