The equally spaced energy levels of the quantum harmonic oscillator revisited: a back-to-front reconstruction of an n-body Hamiltonian
journal contributionposted on 2017-10-02, 12:36 authored by Terry Robinson
The "back-to-front" derivation of the properties of the quantum harmonic oscillator, starting with its equally spaced energy levels is re-examined. A new derivation that exploits the natural rotational symmetry of the quantum harmonic oscillator is proposed. The new approach allows the "back-to-front" idea to be extended further by showing that it is possible to derive the Hamiltonian of a system of particles from the starting point that the population is represented by a natural number. This involves the symmetry properties of phasors and Schwinger's theory of angular momentum. The analysis is also extended to multi-mode bosonic systems and fermionic systems. It is suggested that these results offer an alternative way to formulate physics, based on discreteness.
CitationEuropean Journal of Physics, 2017, in press
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Physics and Astronomy
- AM (Accepted Manuscript)