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The effect of fractional calculus on the formation of quantum-mechanical operators
- Issue Date
- 30-Jul-2020
- Publisher
- John Wiley & Sons Inc.
- Keywords
- the fractional calculus; the fractional quantum mechanics; the fractional wave equation
- Citation
- Mathematical Methods in the Applied Sciences, v.43, no.11, pp 6950 - 6967
- Pages
- 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- Mathematical Methods in the Applied Sciences
- Volume
- 43
- Number
- 11
- Start Page
- 6950
- End Page
- 6967
- ISSN
- 0170-4214
1099-1476
- Abstract
- 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.
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