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- Thread starter Viorel Popescu
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bhobba

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Hi

Ae^i(kx - wt) in suitable units is a solution and is not normalizeable.

So you cant always normalize it. The solution lies in what's called Rigged Hilbert Spaces.

At the intuitive level you consider it as an approximation to one that is ie assuming a finite universe at some very large distance it is zero. But rigorously it requires what I said - Rigged Hilbert Spaces.

As a warm-up up I highly recommend the following book:

https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20&tag=pfamazon01-20

All physicists, and indeed applied mathematicians need to know this stuff. It's worth it for its treatment of Fourier Transforms alone - otherwise you get bogged down in issues of convergence, providing of course you want to have at least a reasonable level of rigor and not hand-wavy - which IMHO is the same as the intuitive view I gave before. Its OK to start with but as you progress you will want a better understanding.

Thanks

Bill

Ae^i(kx - wt) in suitable units is a solution and is not normalizeable.

So you cant always normalize it. The solution lies in what's called Rigged Hilbert Spaces.

At the intuitive level you consider it as an approximation to one that is ie assuming a finite universe at some very large distance it is zero. But rigorously it requires what I said - Rigged Hilbert Spaces.

As a warm-up up I highly recommend the following book:

https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20&tag=pfamazon01-20

All physicists, and indeed applied mathematicians need to know this stuff. It's worth it for its treatment of Fourier Transforms alone - otherwise you get bogged down in issues of convergence, providing of course you want to have at least a reasonable level of rigor and not hand-wavy - which IMHO is the same as the intuitive view I gave before. Its OK to start with but as you progress you will want a better understanding.

Thanks

Bill

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