Energy Levels of 'Hydrogen Atom' in Discrete Time Dynamics

Journal Article · Wed Jan 04 00:00:00 EST 2006 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2158749· OSTI ID:20787712

Khrennikov, Andrei; Volovich, Yaroslav ^[1]

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1. International Center for Mathematical Modeling in Physics, Engineering and Cognitive science, MSI, Vaexjoe University, S-35195 (Sweden)

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time{exclamation_point}) dynamics is compatible with discrete energy levels.

• OSTI ID: 20787712
• Journal Information: AIP Conference Proceedings, Vol. 810, Issue 1; Conference: Vaxjo conference on quantum theory: Reconsideration of foundations - 3, Vaxjo (Sweden), 6-11 Jun 2005; Other Information: DOI: 10.1063/1.2158749; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
CENTRAL POTENTIAL
ENERGY LEVELS
ENERGY SPECTRA
HARMONIC OSCILLATORS
HYDROGEN
QUANTUM MECHANICS