What notation would mathematicians use ?

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Discussion Overview

The discussion revolves around the notation used by mathematicians, particularly in the context of quantum mechanics and Hilbert spaces. Participants explore different representations of the identity operator and the concept of rigged Hilbert spaces.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks how a mathematician would express the identity operator using integrals and bra-ket notation.
  • Another participant suggests an alternative notation involving a projector acting on a rigged Hilbert space.
  • A question is raised about the definition and structure of a rigged Hilbert space.
  • A subsequent reply provides a description of a rigged Hilbert space as a set of four spaces.
  • One participant indicates that their previous comment was made in jest.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints regarding the notation and definitions, with no consensus reached on the preferred notation or the understanding of rigged Hilbert spaces.

Contextual Notes

Participants do not clarify certain assumptions about the notation or the properties of rigged Hilbert spaces, leaving some aspects unresolved.

TOKAMAK
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How would a mathematician write this:

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

[tex]\hat{1}=\int dx \ \hat{P}_{x}[/tex]

,where the projector acts on a rigged Hilbert space.

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

[tex]\Omega\subset\mathcal{H}\cong \tilde{\mathcal{H}}\subset \tilde{\Omega}[/tex]

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

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