What are the minimal conditions to have a non-relativistic quantum theory like Schrödinger theory?
What do you mean by conditions? Mathematical conditions? Axioms?
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.
Is [x,t]≠0 compatible with a time-evolution operator.
But t is not a dynamic observable.
What do you mean orienst?
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.
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