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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

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2024

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Vol. 28, No 1

1--16

EN

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.

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Systems of free particles and harmonic oscillators in rotationally-invariant noncommutative phase space

Gnatenko Khrystyna P., Tkachuk Volodymyr M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2023

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Vol. 27, No 3

1--13

EN

In this paper, we introduce a rotationally-invariant noncommutative algebra that is equivalent to the canonical type.This algebra is built by extending the noncommutativity parameters to tensors. These tensors are defined with the help of additional coordinates and momenta corresponding to a rotationally-invariant system. In the frame of the rotationally-invariant noncommutative algebra we investigate a system of free particles, and systems of harmonicoscillators. The energy levels of these systems are found in noncommutative phase spave with preserved rotational symmetry.

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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

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2023

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Vol. 27, No 4

1--8

EN

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.

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The Soccer-Ball Problem in Quantum Space

Gnatenko Khrystyna P., Tkachuk Volodymyr M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2019

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Vol. 23, No 4

361--450

EN

The monograph is devoted to studies of the problem of a macroscopic body known as the soccer-ball problem in the frame of different deformed algebras leading to space quantization. It is shown that this problem can be solved in a deformed space with a minimal length, in a noncommutative phase space, in a space with a Lie-algebraic noncommutativity, in a twist-deformed space-time due to the relation of parameters of corresponding algebras with mass. In addition, we conclude that this relation gives a possibility to obtain a list of important results in quantum space including recovering the weak equivalence principle, preserving the properties of the kinetic energy, obtaining the Galilean and Lorentz transformations independent of the mass of the particle.