ELFT HÍRADÓ

[Király Beáta <kiraly.beata AT atomki.hu>]

Analytic solutions of the complex diffusion equation with aspects on quantum 
mechanics 

by Barna Imre Ferenc 
HUN-REN Wigner Research Centre for Physics > Institute for Particle and 
Nuclear Physics > High-energy Physics Department > Laser Particle Accelerator 
Technology Research Group 



When: 2025-09-18 Thursday 11:00 

Where: HUN-REN ATOMKI, nagyelőadó (Debrecen, Bem tér 18/c) 





Other information: 
Tea and cookies are offered 30 minutes before the seminar. 



Abstract: 
In our study, we derive and compare the solutions of the real and complex 
diffusion equations obtained by the self-similar solution to each other. 
Additionally, possible quantum mechanical aspects are analyzed as well. In 
the second part of the study, a complex reaction diffusion equation is 
investigated and compared to the quantum mechanical solutions of the 
corresponding Schrödinger equation with a power-law-type potential. We show 
that the same parameter ratio emerges in the quantum mechanical and the 
self-similar solutions as well, which is a remarkable property. For both 
investigated equations, the complex diffusion and complex reaction diffusion 
equations, we found some solutions for which the absolute value squared has a 
convergent-finite numerical integral. This is not a rigorous L 2 
integrability condition but a good hint for that, which is a key property in 
quantum mechanics. In the final part of our talk we investigate the spherical 
symmetric case as well. 









--- 
Király Beáta, PhD 
HUN-REN ATOMKI / HUN-REN Atommagkutató Intézet 
C: 4026 Debrecen, Bem tér 18/c 
T: +36 52 509 200 
E: kiraly.beata AT atomki.hu 
W: [ http://www.atomki.hu/ | www.atomki.hu ]