The effect of fractional calculus on the formation of quantum‐mechanical operators
Won Sang Chung, Soroush Zare, H. Hassanabadi, Elham Maghsoodi
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.
Topics & Concepts
Fractional calculusMathematicsHarmonic oscillatorLorentz transformationQuantum harmonic oscillatorCalculus (dental)Mathematical physicsSupersymmetric quantum mechanicsQuantumClassical mechanicsQuantum statistical mechanicsQuantum mechanicsMathematical analysisPhysicsMedicineDentistryFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical and Theoretical Analysis