A NOVEL PERSPECTIVE FOR THE FRACTAL SCHRÖDINGER EQUATION
Kang‐Le Wang
Abstract
In this work, the Schrödinger equation is described by the fractal derivative, and its variational principle is obtained by using the fractal semi-inverse method. The variational principle is helpful to research the construction of the solution. The approximate analytical solution of the fractal Schrödinger equation is obtained based on the proposed variational approach and the fractal two-scale transform method. Finally, an example shows that the proposed approach is very fascinating in deal with nonlinear fractal models.
Topics & Concepts
FractalFractal derivativeMathematicsVariational principleApplied mathematicsNonlinear systemInverseSchrödinger equationWork (physics)Mathematical analysisNonlinear Schrödinger equationPerspective (graphical)Fractal analysisFractal dimensionPhysicsGeometryQuantum mechanicsFractional Differential Equations SolutionsStatistical Mechanics and EntropyNonlinear Waves and Solitons