1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wavefunctions of hydrogen

  1. May 2, 2014 #1
    1. The problem statement, all variables and given/known data

    29kx94y.png

    What quantum numbers are used to define state of hydrogen? The wavefunction has no angular dependence. Find the values of all the angular momentum quantum numbers for the electron.

    2. Relevant equations



    3. The attempt at a solution

    The numbers are n, l and m.

    n: Energy level
    l(l+1): Eigenvalues of total orbital angular momentum
    m: z component of orbital angular momentum

    The complete wavefunction is given by: ##\psi = u_n^l Y_l^m##.

    Thus the only spherical harmonic that doesn't have angular dependence is ##Y_0^0 = \sqrt{\frac{1}{4\pi}}##.

    Thus the wavefunctions are ##\sqrt{\frac{1}{4\pi}}u_n^0##.

    Thus n = any integer, l = 0, m = 0.

    I'm slightly bothered by the term 'spatial part' of the wavefunction.
     
  2. jcsd
  3. May 3, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    "Spatial part" as opposed to "spin part". The exercise probably doesn't want you to worry about spin (my guess -- change that if you just finished a chapter on spin...)
     
  4. May 3, 2014 #3
    We learn about the gross structure of Hydrogen, which ignores spin as the Hamiltonian is the KE of the nucleus and electron, and the potential energy.

    Are my answers right then?
     
  5. May 4, 2014 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I would say yes. A nitpicker would argue n isn't a quantum number for angular momentum. In that case the answer is: l = 0 and m = 0
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Wavefunctions of hydrogen
  1. Hydrogen wavefunctions (Replies: 0)

Loading...