Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

Details Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

2006-04-27

arxiv.org/abs/quant-ph/0604199v1

Physics

Quantum Physics

accepted for publication in Open Systems & Information Dynamics

Scientific paper

10.1063/1.2158749

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!) dynamics is compatible with discrete energy levels.

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