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

[Mokdad]

What are the minimal conditions to have a non-relativistic quantum theory like Schrödinger theory?

 

[tom.stoer]

What do you mean by conditions? Mathematical conditions? Axioms?

 

[Mokdad]

mathematical conditions.

 

[tom.stoer]

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.

 

[Mokdad]

Thank you.
Is [x,t]≠0 compatible with a time-evolution operator.

 

[orienst]

But t is not a dynamic observable.

 

[Mokdad]

What do you mean orienst?

 

[tom.stoer]

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.