Version 1
: Received: 6 December 2023 / Approved: 14 December 2023 / Online: 15 December 2023 (03:35:47 CET)
How to cite:
Barna, I.F.; Mátyás, L. Analytic Solutions of the Complex Diffusion Equation with
Possible Quantum Mechanical Relevance. Preprints2023, 2023121091. https://doi.org/10.20944/preprints202312.1091.v1
Barna, I.F.; Mátyás, L. Analytic Solutions of the Complex Diffusion Equation with
Possible Quantum Mechanical Relevance. Preprints 2023, 2023121091. https://doi.org/10.20944/preprints202312.1091.v1
Barna, I.F.; Mátyás, L. Analytic Solutions of the Complex Diffusion Equation with
Possible Quantum Mechanical Relevance. Preprints2023, 2023121091. https://doi.org/10.20944/preprints202312.1091.v1
APA Style
Barna, I.F., & Mátyás, L. (2023). Analytic Solutions of the Complex Diffusion Equation with
Possible Quantum Mechanical Relevance. Preprints. https://doi.org/10.20944/preprints202312.1091.v1
Chicago/Turabian Style
Barna, I.F. and László Mátyás. 2023 "Analytic Solutions of the Complex Diffusion Equation with
Possible Quantum Mechanical Relevance" Preprints. https://doi.org/10.20944/preprints202312.1091.v1
Abstract
In our latest studies with the help of the self-similar Ansatz we derived new type of 1
solutions for the regular diffusion equation which are much more complex than the well-known 2
Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3
functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4
regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5
the free Schrödinger equation however it is far from being trivial how the solutions can be given 6
quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7
spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8
might have quantum mechanical relevance in the future.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
