Exact solutions of the Schrödinger–Dunkl equation for a free particle in a finite and infinite cylindrical well

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Analysis reveals energy spectra and wavefunctions for particles in cylindrical potential wells, indicating the effects of Dunkl parameters.

Exact analytical expressions for wavefunctions are derived using Bessel functions for cylindrical coordinates.
The study shows wavefunctions' parity is influenced by reflection operators, altering the Hamiltonian structure.
Cylindrical potential wells are classified by energy spectra based on the eigenvalues of reflection operators.
Dunkl parameters impose constraints on wavefunctions, highlighting conditions for definite parity.

Mota et al. (2025) studied this question.

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Analysis reveals energy spectra and wavefunctions for particles in cylindrical potential wells, indicating the effects of Dunkl parameters.