The Paradigm of Complex Probability and Quantum Mechanics: The Infinite Potential Well Problem - The Momentum Wavefunction and the Wavefunction Entropies

Abdo Abou Jaoude

A chapter in Applied Probability Theory - New Perspectives, Recent Advances and Trends from IntechOpen

Abstract: The mathematical probability concept was set forth by Andrey Nikolaevich Kolmogorov in 1933 by laying down a five-axioms system. This scheme can be improved to embody the set of imaginary numbers after adding three new axioms. Accordingly, any stochastic phenomenon can be performed in the set C of complex probabilities which is the summation of the set R of real probabilities and the set M of imaginary probabilities. Our objective now is to encompass complementary imaginary dimensions to the stochastic phenomenon taking place in the "real" laboratory in R and as a consequence to calculate in the sets R, M, and C all the corresponding probabilities. Hence, the probability is permanently equal to one in the entire set C = R+M independently of all the probabilities of the input stochastic variable distribution in R, and subsequently, the output of the random phenomenon in R can be determined perfectly in C. This is due to the fact that the probability in C is calculated after the elimination and subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic phenomenon. My innovative Complex Probability Paradigm (CPP) will be applied to the established theory of quantum mechanics in order to express it completely deterministically in the universe C=R+M.

Keywords: degree of our knowledge; chaotic factor; complex random vector; probability norm; complex probability set C; momentum wavefunction; imaginary entropy; complex entropy (search for similar items in EconPapers)
JEL-codes: C25 C83 (search for similar items in EconPapers)
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.intechopen.com/chapters/84705 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:289545

DOI: 10.5772/intechopen.107665

Access Statistics for this chapter

More chapters in Chapters from IntechOpen
Bibliographic data for series maintained by Slobodan Momcilovic (ai@intechopen.com).