Branch Mathematics and Statistics Faculty and Staff Publications
A Numerical Solution of Ermakov Equation Corresponding to Diffusion Interpretation of Wave Mechanics
Document Type
Preprint
Publication Date
Summer 7-4-2017
Abstract
It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.
Language (ISO)
English
Recommended Citation
Christianto, Victor and Florentin Smarandache. "A Numerical Solution of Ermakov Equation Corresponding to Diffusion Interpretation of Wave Mechanics." (2017). https://digitalrepository.unm.edu/math_fsp/637
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
