- #1

Niles

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## Homework Statement

Hi all.

The inner product between two functions f(x) and g(x) is defined as:

[tex]

<f | g> = \int f^*(x)g(x) dx,

[/tex]

where the * denotes the complex conjugate. Now if my functions f and g are functions of r, theta and phi (i.e. they are written in spherical coordinates), is the volume element then given as [itex]drd\theta d\phi[/itex] or [itex]r^2\sin \theta drd\theta d\phi[/itex]?

## The Attempt at a Solution

I personally think the last, because originally we have <f(x,y,z) | g(x,y,z)>, which we convert to spherical coordinates, so we need the Jacobian. Am I correct?

Thanks in advance.