A question about fourier analysis

rar0308
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Hi.
see the image.
In the integral there's no dx,dy,dz thing. Does this make any sense?
Isn't it errata?
 

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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...
 
Thanks.
It's from page 11 <Quantum Theory> David Bohm, Dover.
 
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.
 
daveyp225 said:
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?
 
pwsnafu said:
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.
 

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