- #1

- 7

- 0

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?

- Thread starter MontavonM
- Start date

- #1

- 7

- 0

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

- 649

- 3

yeah, over a whole period, or the appropriate bounds.

- #3

strangerep

Science Advisor

- 3,168

- 1,013

That looks like the wrong measure for spherical polar coordinates.

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?

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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