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Orthonormal wavefunctions?

  1. Oct 1, 2011 #1
    Given 2 wavefunctions with respect to (r,theta,phi)...

    To prove that the functions are orthonormal, you would let the first w.function = Y(psi) and the 2nd = Y* (psi star), then you would integrate --> SY*Y dr dtheta dphi (integral of psi* times psi) dr dtheta dphi.

    Correct?
     
  2. jcsd
  3. Oct 1, 2011 #2
    yeah, over a whole period, or the appropriate bounds.
     
  4. Oct 1, 2011 #3

    strangerep

    User Avatar
    Science Advisor

    That looks like the wrong measure for spherical polar coordinates.
    I would have expected something like:
    [tex]
    \int_0^{2\pi} d\phi \int_0^\pi \sin\theta \; d\theta \int_0^\infty \bar f g \, r^2 dr
    [/tex]
    where f,g are functions of [itex]r,\theta,\phi[/itex].

    See also:

    http://en.wikipedia.org/wiki/Volume_integral
     
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