This book is titled “The Paradigm of Complex Probability and Quantum Mechanics”. It includes a creative work that illustrates my novel and original “Complex Probability Paradigm”, or CPP for short, when applied to four famous problems in Quantum Mechanics which are: The Infinite Potential Well Problem, The Quantum Harmonic Oscillator with Gaussian Initial Condition, The Heisenberg’s Quantum Uncertainty Principle, and The Quantum Entropic Uncertainty Principle. Consequently, six chapters were written for this purpose where the paradigm was implemented to the position wavefunction of the Infinite Potential Well Problem first, to the momentum wavefunction and to the wavefunction entropies of the Infinite Potential Well Problem second, to the position wavefunction of the Quantum Harmonic Oscillator with Gaussian Initial Condition third, to the momentum wavefunction and to the wavefunction entropies of the Quantum Harmonic Oscillator with Gaussian Initial Condition fourth, to Heisenberg’s Quantum Uncertainty Principle fifth, and to the Quantum Entropic Uncertainty Principle sixth.
In fact, my background is a Ph.D. in Computer Science, a Ph.D. in Applied Mathematics, and a Ph.D. in Applied Probability and Statistics, so I combined my knowledge in Probability Theory with Applied Mathematics and I wrote this book and this mathematical and physical and philosophical model and paradigm. Actually, as it is well-known, that the theorems and the theories of Quantum Mechanics are the work of eminent mathematicians and physicists like the legends Albert Einstein, Niels Bohr who was the founder and the head of the Copenhagen research group and institute at the beginning of the twentieth century, Max Planck, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac, Louis de Broglie, David Bohm, John Stewart Bell, Emmy Noether, etc.
Thus, we must pay tribute to those magnificent giants of science and sometimes of philosophy who contributed to enrich our knowledge of mathematics and physics and the universe and increased our understanding of all-natural phenomena and of existence.
Moreover, to introduce and to summarize this new paradigm to the reader we state that: the great Russian mathematician Andrey Nikolaevich Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm is to add new imaginary dimensions to the experiment real dimensions that occur in the “real” laboratory which will make the work in the complex probability set C totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities R the contributions of the imaginary set of probabilities M will make the event in C = R + M absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Consequently, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the real and imaginary and complex probabilities in the probability sets R and M and C and which are all subject to chaos and random effects. Accordingly, by subtracting the chaotic factor from the degree of our knowledge of the stochastic system, we evaluate the probability of any random phenomenon, like in Quantum Mechanics, in C. Therefore, since this extension was found to be successful and fruitful, then a novel paradigm of stochastic sciences and prognostic and mathematics and science in general was set forth in which all stochastic phenomena in R was expressed entirely deterministically in C = R + M. This is what I coined by the terms “The Complex Probability Paradigm”.
Additionally, my pioneering paradigm was the subject of 25 international journals papers and books chapters published since 2010 till 2023 like with Taylor and Francis and with IntechOpen, London, United Kingdom.
Furthermore, the book uses hence algorithms to simulate my applied paradigm to random phenomena encountered in Quantum Mechanics. They were executed on my workstation computer system to acquire a suitable speed and efficiency needed for this numerical and stochastic method and I wrote them using the well-known software which is MATLAB version 2023.
Likewise, in January 2023, I have done an interview with the platform named Faculti located in London, United Kingdom, where I have discussed upon their request my published paper in 2018 with Taylor and Francis and which is: “The Paradigm of Complex Probability and Ludwig Boltzmann’s Entropy”. It lasts about 20 minutes. So, you can surely log in the website of Faculti and watch it for free.
To conclude, as I have mentioned in many previous books and publications, I repeat and say that due to its universality mathematics is the most positive and certain branch of science. Surely, the pleasure of working and doing mathematics and physics is everlasting. I hope that the reader will benefit from both and share the pleasure of examining the present manuscript. Finally, I restate also my words to affirm that the combination of both mathematics and physics and science in general leads to “magical” and amazing results and models and philosophical paradigms, and the following work is an illustration of this approach.
