A question about fourier analysis

[rar0308]

Hi.
see the image.
In the integral there's no dx,dy,dz thing. Does this make any sense?
Isn't it errata?

 

[mathfeel]

It is wrong without the dx, dy, dz thing. If this comes from some hand written note, it's usually implied. If this comes from a book, you need to kick the editor in the nut...

 

[rar0308]

Thanks.
It's from page 11 <Quantum Theory> David Bohm, Dover.

 

[daveyp225]

It makes sense if the order does not matter for integration. If it is obvious in context that the variables here are x,y,z (L is clearly a constant as integrals contain it) and Fubini's Theorem is satisfied then you are free to choose.

 

[pwsnafu]

It makes sense if the order does not matter for integration. If it is obvious in context that the variables here are x,y,z (L is clearly a constant as integrals contain it) and Fubini's Theorem is satisfied then you are free to choose.

How do you know that l, m, n, l', m', n' are constant?

 

[daveyp225]

How do you know that l, m, n, l', m', n' are constant?

I said "if it was obvious in context the variables are x, y and z". Otherwise, call it a good hunch, as there are only three integration variables present and the ' notation often signifies a relationship between, for example, m and m'. All six cannot be integration variables, and if the first three were then the second sine function is only a constant with respect to integration and would probably not be part of the integrand.