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2 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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Hydrogen and exotic atoms in rotationally-invariant space with noncommutativity of coordinates and noncommutativity of momenta

Gnatenko Khrystyna P., Tkachuk Volodymyr M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2024

Vol. 28, No 1

1--16

The effect of the noncommutativity of coordinates and noncommutativity of momenta on the spectrum of the hydrogen atom is studied. Corrections to the energy levels of the atom up to the second order in the parameter of noncommutativity are found. Based on the obtained results and the experimental data for the1S−2Stransition frequency, the upper bound for the minimal length is obtained. Also, a two-particle system with Coulomb interaction is examined and hydrogen-like exotic atoms are studied in rotationally-invariant noncommutative phase space.

System of harmonic oscillators in a rotationally-invariant noncommutative phase space

Gnatenko Khrystyna P., Tkachuk Volodymyr M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2023

Vol. 27, No 4

1--8

Algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally-invariant and equivalent to noncommutative algebra of the canonical type is considered. In the framework of algebra, the effect of space quantization on the spectrum of systems of harmonic oscillators is studied. Among them, two interacting oscillators, a system of three interacting oscillators, and a harmonic oscillator chain are examined. The energy levels of the systems are found up to the second orders in the parameters of noncommutativity. We conclude that space quantization has an effect on the frequencies of the harmonic oscillators.