The Quantum Harmonic Oscillator in the ESR Model

TL;DR

This paper extends the ESR model's noncontextual framework to the quantum harmonic oscillator, reinterpreting probabilities and state transformations within this new formalism.

Contribution

It applies the ESR model to the quantum harmonic oscillator, providing new probability expressions and modified state transformation rules.

Findings

Reinterpreted quantum probabilities as conditional on detection.

Derived new expressions for absolute probabilities.

Modified state transformation rules in the ESR framework.

Abstract

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.