I State Vectors vs. Wavefunctions

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The discussion centers on the relationship between state vectors in Hilbert space and wavefunctions in L^2 space within quantum mechanics. Participants clarify that while kets (state vectors) and wavefunctions are not identical, they are related through an isomorphism, allowing for a transformation between the two representations. The conversation emphasizes that operators in L^2 can have different forms compared to their representations in Hilbert space, and the need for constructing explicit isomorphisms between linear operators in these spaces is highlighted. Additionally, the distinction between the mathematical objects of wavefunctions and their values at specific points is discussed, underscoring the importance of notation in quantum mechanics. Overall, the dialogue aims to deepen understanding of these foundational concepts in quantum theory.
  • #31
bob012345 said:
My takeaway from this discussion is that the physics sometimes gets lost in the math. Very disheartening when intelligent people can't even agree on the mathematics of quantum theory.

I don't think the disagreement is very deep. It's a disagreement about how best to describe what's going on, but there's no disagreement about how to use the mathematics.
 
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  • #32
stevendaryl said:
I don't think the disagreement is very deep. It's a disagreement about how best to describe what's going on, but there's no disagreement about how to use the mathematics.
What is going on that the mathematical treatments are not agreeing. What is the physics? Thanks.
 
  • #33
bob012345 said:
What is going on that the mathematical treatments are not agreeing.
Nothing. Nobody is disagreeing on what the actual mathematics are. The argument is about how to best define one's notation.
 

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