WKB approximation with conformable operator
Mohamed Ghaleb Al-Masaeed, Eqab M. Rabei, A. Al-Jamel
Abstract
In this paper, the Wentzel–Kramers–Brillouin (WKB) method is extended to be applicable for conformable Hamiltonian systems, where the concept of conformable operator with fractional order [Formula: see text] is involved. The WKB approximation for the [Formula: see text]-wave function is derived for potentials which slowly vary in space. Some illustrative examples to demonstrate the method are presented. The quantities of the conformable form are found to be in exact agreement with the corresponding traditional quantities when [Formula: see text].
Topics & Concepts
WKB approximationConformable matrixPhysicsOperator (biology)Mathematical physicsHamiltonian (control theory)Quantum mechanicsMathematicsTranscription factorChemistryMathematical optimizationRepressorBiochemistryGeneQuantum Mechanics and Non-Hermitian PhysicsFractional Differential Equations SolutionsQuantum chaos and dynamical systems