What notation would mathematicians use ?

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Mathematicians often express the identity operator using notation like \hat{1} = \int dx |x\rangle \langle x|, which represents the resolution of identity in quantum mechanics. The discussion also mentions the use of projectors in a rigged Hilbert space, denoted as \hat{1} = \int dx \ \hat{P}_{x}. A rigged Hilbert space is described as a set of four spaces, including \Omega, \mathcal{H}, \tilde{\mathcal{H}}, and \tilde{\Omega}. The conversation includes playful banter, indicating a lighthearted exchange among participants. Ultimately, the focus remains on the mathematical notation and concepts relevant to quantum mechanics.
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How would a mathematician write this:

\hat{1} = \int dx |x\rangle \langle x| ?
 
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This one,i guess

\hat{1}=\int dx \ \hat{P}_{x}

,where the projector acts on a rigged Hilbert space.

Daniel.
 
What's a rigged Hilbert space dex?
 
As set of 4 spaces

\Omega\subset\mathcal{H}\cong \tilde{\mathcal{H}}\subset \tilde{\Omega}

Daniel.
 
I was just ****in with you :)
 

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