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piareround

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So I was recently learned that for some square integrable position wave-functions in Hilbert Space have the momentum function is not square integrable. Thus the momentum function are not in hilbert space. However, due to "Fourier's Trick" Dirac discovered for quantum mechanics, the momentum functions behave just like if they where square integrable.

Being a curious physics student, I asked my professor more if there was a "special" space these momentum function where in even though they where not in Hilbert Space.

He told me about this thing called http://en.wikipedia.org/wiki/Rigged_Hilbert_space" , which included both the square integrable functions in Hilbert space and their related momentum functions.

I was kind of confused about what he talked about so I was kind of curious to learn more about Rigged Hilbert Space...

Questions:

1. What are the properties of Rigged Hilbert Space compared to Hilbert Space?

2. Are Rigged Hilbert Spaces also Approximate Hilbert Space? Is a Rigged Hilbert Space what we use in Quantum Field Theory when we are talking about the quantum physics of a particle decay state that are not stable states; a problem that where we use use a Approximate Hilbert Space?

3. Are their any books on Rigged Hilbert Space if I wanted to learn more?

Being a curious physics student, I asked my professor more if there was a "special" space these momentum function where in even though they where not in Hilbert Space.

He told me about this thing called http://en.wikipedia.org/wiki/Rigged_Hilbert_space" , which included both the square integrable functions in Hilbert space and their related momentum functions.

I was kind of confused about what he talked about so I was kind of curious to learn more about Rigged Hilbert Space...

Questions:

1. What are the properties of Rigged Hilbert Space compared to Hilbert Space?

2. Are Rigged Hilbert Spaces also Approximate Hilbert Space? Is a Rigged Hilbert Space what we use in Quantum Field Theory when we are talking about the quantum physics of a particle decay state that are not stable states; a problem that where we use use a Approximate Hilbert Space?

3. Are their any books on Rigged Hilbert Space if I wanted to learn more?

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