Orthonormal wavefunctions?

  • Thread starter MontavonM
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  • #1
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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?
 

Answers and Replies

  • #2
649
3
yeah, over a whole period, or the appropriate bounds.
 
  • #3
strangerep
Science Advisor
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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?
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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