https://doi.org/10.1140/epjp/s13360-024-05008-2
Regular Article
Two-parameter deformed quantum mechanics based on Fibonacci calculus and Debye crystal model of two-parameter deformed quantum statistics
1
Department of Mechanical Engineering, Faculty of Technology, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey
2
Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, 660-701, Jinju, Korea
Received:
8
January
2024
Accepted:
14
February
2024
Published online:
28
February
2024
Starting on the basis of Fibonacci calculus and Fibonacci oscillator algebra, we introduce the main properties to develop a new formalism for the two-parameter 
-deformed quantum mechanics, where 
and 
are real positive independent deformation parameters. As applications of such a two-parameter deformed formalism, we investigate the behavior of a quantum particle in some different physical phenomena covering the free particle and the inverse-harmonic potential case. The effect of two deformation parameters on the wave functions for these applications is studied. Another application is carried out onto the quantum statistics of lattice oscillations through a model of the -deformed phonon gas, and it is shown that the high- and low-temperature behavior of the model specific heat differs notably from the classical theories for the interval 
. We also construct a two-parameter deformed non-extensive entropy based on some elements of the Fibonacci calculus and discuss its possible connection with the Tsallis entropy in non-extensive statistical mechanics. Finally, other possible application areas of the present two-parameter -deformed construction on quantum mechanics are discussed.
© The Author(s) 2024
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