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

Click For Summary

Discussion Overview

The discussion revolves around the minimal conditions required for a non-relativistic quantum theory, specifically referencing Schrödinger theory. Participants explore the mathematical framework and foundational aspects of such theories.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks about the minimal conditions for a non-relativistic quantum theory, specifically in the context of Schrödinger theory.
  • Another participant seeks clarification on whether "conditions" refers to mathematical conditions or axioms.
  • A participant identifies mathematical conditions as necessary, mentioning the need for a separable Hilbert space, hermitian operators for observables, and a time-evolution operator.
  • There is a question about the compatibility of the commutation relation [x,t]≠0 with a time-evolution operator.
  • One participant asserts that time (t) is not a dynamic observable, but rather a parameter in the theory.
  • Another participant elaborates that in quantum mechanics, observables are represented by hermitian operators, but emphasizes that time is not treated symmetrically with space in non-relativistic quantum mechanics.

Areas of Agreement / Disagreement

Participants express differing views on the role of time as an observable and its implications for non-relativistic quantum mechanics. The discussion does not reach a consensus on the compatibility of certain mathematical conditions.

Contextual Notes

There are unresolved questions regarding the definitions of observables and the implications of treating time as a parameter rather than a dynamic observable. The discussion also touches on the limitations of non-relativistic quantum mechanics compared to relativistic frameworks.

Mokdad
Messages
6
Reaction score
0
What are the minimal conditions to have a non-relativistic quantum theory like Schrödinger theory?
 
Physics news on Phys.org
What do you mean by conditions? Mathematical conditions? Axioms?
 
mathematical conditions.
 
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.
 
Thank you.
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.
 

Similar threads

Graduate Consistency of Relativistic QM
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Multiparticle Relativistic Quantum Mechanics in an external potential
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad What are anomalies in quantum field theory?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Different expressions about time reversal and confusion
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Is quantum theory a microscopic theory?
  • · Replies 232 ·
8
Replies
232
Views
22K
Graduate Exact symmetry, quantum states, and symmetric dynamics
  • · Replies 8 ·
Replies
8
Views
1K
High School Quantum Field Theory As Simple As Possible
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Klein-Gordon equation in the nonrelativistic limit
  • · Replies 3 ·
Replies
3
Views
1K
Graduate QFT with vanishing vacuum expectation value and perturbation theory
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Why does QM split into two evolution types?
  • · Replies 7 ·
Replies
7
Views
484