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 L² 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.

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