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Journal of Physical Studies 25(2), Article 2002 [6 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.2002 PARTICLE IN A UNIFORM FIELD IN A NONCOMMUTATIVE SPACE WITH PRESERVED TIME REVERSAL AND ROTATIONAL SYMMETRIES
Kh. P. Gnatenko
Ivan Franko National University of Lviv, Department for Theoretical Physics,
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The paper studies quantized space described by a time reversal invariant and rotationally invariant noncommutative algebra of a canonical type. A particle in a uniform field is considered. We find exactly the energy of a particle in a uniform field in the quantized space and its wavefunctions. It is shown that the motion of the particle in the field direction in time reversal invariant and rotationally invariant noncommutative space is the same as in an ordinary space (a space with the ordinary commutation relations for the operators of coordinates and the operators of momenta). The noncommutativity of the coordinates has an influence only on the motion of the particle in the directions perpendicular to the field direction. Namely, space quantization has an effect on the mass of the particle.
Key words: quantized space, noncommutative coordinates, time reversal symmetry, rotational symmetry, particle in uniform field
