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Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
Martin Plávala1, Matthias Kleinmann1,2
1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany.
Physical Review Letters
|February 11, 2022
Summary
This study introduces a method for building probabilistic theories with energy observables, applicable to classical and quantum mechanics. A novel toy model demonstrates these theories
Area of Science:
- Theoretical physics
- Foundations of physics
- Probabilistic theories
Background:
- Classical and quantum mechanics provide frameworks for physical theories.
- Existing theories describe energy observables in relation to position and momentum.
- There is a need for alternative frameworks to explore physical phenomena.
Purpose of the Study:
- To develop a method for constructing general probabilistic theories.
- To incorporate energy observables dependent on position and momentum.
- To demonstrate the viability of operational theories in physics.
Main Methods:
- Constructing general probabilistic theories.
- Defining energy observables dependent on position and momentum.
- Formulating a toy model for the harmonic oscillator.
Main Results:
- The construction aligns with classical and quantum theory.
- Physical predictions for position, momentum, and energy distributions are possible.
- A toy model exhibits a discrete energy spectrum, a ground state with sharp position and momentum, and tunneling properties.
Conclusions:
- Operational theories offer a viable alternative for formulating physical theories.
- The developed framework allows for predictions in novel theoretical models.
- The toy model highlights unique features not present in classical or quantum mechanics.
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