Foundations of Physics

, Volume 43, Issue 6, pp 792–804

The Quantum Harmonic Oscillator in the ESR Model


DOI: 10.1007/s10701-013-9717-5

Cite this article as:
Sozzo, S. Found Phys (2013) 43: 792. doi:10.1007/s10701-013-9717-5


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.


Quantum mechanics Harmonic oscillator State transformations ESR model 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Center Leo Apostel (CLEA)Brussels Free University (VUB)BrusselsBelgium
  2. 2.Department of Mathematics and PhysicsUniversity of SalentoLecceItaly

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