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Superposition of spherical harmonics

  1. Apr 4, 2015 #1
    i am a beginner and was going through (Donald Mcquarie's "quantum chemistry" ) some discussion regarding orbitals of H-atom but i didn't get the logic behind writing px and py orbitals as linear combinations of spherical harmonics????

    according to what i understood, a given spherical harmonic in itself represents a orbital depending upon n,l,m ..then how can we write a spherical harmonic as a sum of other two or spherical harmonics with same n,l.

    [Mentor's note: moved from "New Member Introduction" forum to here]
    [Mentor's note: title changed to be more descriptive]
    Last edited by a moderator: Apr 4, 2015
  2. jcsd
  3. Apr 4, 2015 #2
    px = (1/sqrt2)*(Y11+ Y1-1)
    py=(1/sqrt2*i)(Y11- Y1-1)
  4. Apr 4, 2015 #3


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    Staff: Mentor

    Welcome to PF! This forum "New Member Introductions" is for only new member introductions and some chit-chat. Real questions belong in one of our topical forums, such as our "Quantum Physics" forum:


    Please re-post your question there. More people who can actually help you hang out there, as opposed to the few people who hang out here greeting new members.
  5. Apr 5, 2015 #4


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    Science Advisor

    In hydrogen, the spherical harmonics with the same n are all energetically degenerate, so any linear combination is again a solution of the Schrödinger equation. However in molecules, the potential is perturbed and some linear combinations are better zeroth order solutions than others.
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