What are the minimal conditions for a non-relativistic quantum theory?

In summary, the minimal conditions for a non-relativistic quantum theory like Schrödinger theory include a separable Hilbert space, hermitian operators representing observables, and a time-evolution operator. The concept of axioms is also relevant in this approach, with researchers such as Neumann and Weyl studying them. However, t is not considered a dynamic observable in quantum mechanics, unlike x, p, L, and H. This means that [x,t]≠0 is not compatible with a time-evolution operator, and relativistic quantum mechanics would need to be used for symmetry regarding space and time."
  • #1
Mokdad
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What are the minimal conditions to have a non-relativistic quantum theory like Schrödinger theory?
 
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  • #2
What do you mean by conditions? Mathematical conditions? Axioms?
 
  • #3
mathematical conditions.
 
  • #4
Roughly speaking you need a separable Hilbert space, hermitian operators representing observables and a time-evolution operator.

I am not an expert regarding the axiomatic approach.

Neumann studies axioms, Weyl as well.
 
  • #5
Thank you.
Is [x,t]≠0 compatible with a time-evolution operator.
 
  • #6
But t is not a dynamic observable.
 
  • #7
What do you mean orienst?
 
  • #8
In qm you have observables represented by hermitean operators like x, p, angular momentum L, Hamiltonian H. But t is not a dynamacila observable, just a kind of parameter. Non-relativistic qm is not symmetric regarding space and time; you would have to use relativistic quantum mechanics.
 

FAQ: What are the minimal conditions for a non-relativistic quantum theory?

What is the uncertainty principle in quantum theory?

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What is the role of probability in quantum theory?

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What are the implications of quantum theory for technology?

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