1. The problem statement, all variables and given/known data 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]? 3. 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.