Premium
The effect of fractional calculus on the formation of quantum‐mechanical operators
Author(s) -
Chung Won Sang,
Zare Soroush,
Hassanabadi Hassan,
Maghsoodi Elham
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6445
Subject(s) - fractional calculus , mathematics , harmonic oscillator , lorentz transformation , quantum harmonic oscillator , calculus (dental) , mathematical physics , supersymmetric quantum mechanics , quantum , classical mechanics , quantum statistical mechanics , quantum mechanics , mathematical analysis , physics , medicine , dentistry
In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed.