Fractal Schr\"{o}dinger Equation: Implications for Fractal Sets
- URL: http://arxiv.org/abs/2310.16864v1
- Date: Wed, 25 Oct 2023 08:55:15 GMT
- Title: Fractal Schr\"{o}dinger Equation: Implications for Fractal Sets
- Authors: Alireza Khalili Golmankhaneh, Stergios Pellis, Massimiliano Zingales
- Abstract summary: This paper delves into the world of fractal calculus, investigating its implications for fractal sets.
It introduces the Fractal Schr"odinger Equation and provides insights into its consequences.
By intertwining quantum mechanics and fractal mathematics, this research paves the way for deeper insights into their relationship.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper delves into the world of fractal calculus, investigating its
implications for fractal sets. It introduces the Fractal Schr\"{o}dinger
Equation and provides insights into its consequences. The study presents a
General Solution for the Time-Dependent Schr\"{o}dinger Equation, unveiling its
core aspects. Exploring quantum mechanics in the context of fractals, the paper
analyzes the Probability Density of the Radial Hydrogen Atom, unveiling its
behavior within fractal dimensions. The investigation extends to deciphering
the intricate Energy Levels of the Hydrogen Atom, uncovering the interplay of
quantum mechanics and fractal geometry. Innovatively, the research applies the
Fractal Schr\"{o}dinger Equation to Simple Harmonic Motion, leading to the
introduction of the Fractal Probability Density Function for the Harmonic
Oscillator. The paper employs a series of illustrative figures that enhance the
comprehension of the findings. By intertwining quantum mechanics and fractal
mathematics, this research paves the way for deeper insights into their
relationship.
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