Mathematical Foundations of Quantum Mechanics: New Edition

Neumann, J. v., Wheeler, N. A.

John von Neumann

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.

Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics —a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. This new edition of this classic work has been completely reset in TeX, making the text and equations far easier to read. The book has also seen the correction of a handful of typographic errors, revision of some sentences for clarity and readability, provision of an index for the first time, and prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson have been added. The result brings new life to an essential work in theoretical physics and mathematics.

Anders Wimo

Alfred Landé

Musabbiha Haroon Khan Haroon Khan

Quantum Bayesianism and Beyond: Statistical and Bayesian Inference in Complex Quantum Systems, Comprehensive Edition: The book by Musabbiha Haroon introduces Quantostats, a new framework for statistical and Bayesian inference grounded in quantum mechanics and mathematical complexity. This framework employs delta and beta rules to address real-world problems, offering a novel approach that extends beyond traditional inference methods. The book begins with Chapter 0: The Foundation of Evidence, which uniquely starts from the Feynman–Kac path integral rather than conventional Bayesian or statistical inference. Subsequent chapters build a mathematical bridge through concepts such as Wick rotation and the Euler formula, gradually revealing the statistical foundations in Chapter 4, which is followed by Chapter 5, which serves as the foundational core of Quantostats. Early Bayesian updating appears in Chapter 2, while specialised developments, such as the unique Chapter 6.5, were introduced to strengthen the structure when Chapter 10 presented the Whittle likelihood. To balance this, Chapter 9 explores Abel’s theorem, Chapter 14.5 tells the foundational chain of every chapter before and Bounds in Chapter 15, ensuring coherence within the framework. The book’s evolution reflects the author’s independent research journey. An initial unpublished edition spanned 23 chapters but was later condensed and rewritten into the current Extended Edition, which served as a pre-publication draft for the author and preserves the author's copyrights, the result of eight iterations. This final version comprises 14 carefully structured chapters, representing a refined synthesis of statistical analysis, stochastic calculus, Bayesian inference, physics, and complex mathematics, while the Comprehensive Edition was completed as the theoretical and mathematical expansion of the Extended Edition, which expands the framework in advanced mathematical chains Created without institutional affiliation or academic supervision, this work embodies the author’s dedication to advancing statistical and quantum methodologies. It is intended for researchers, students, and practitioners interested in the intersection of quantum mechanics, Bayesian inference, and complex systems. YOU CAN READ THE RESEARCH BOOK DRAFT THROUGH THE ZENODO LINK: https://doi.org/10.5281/zenodo.21325371 FOR THE FIGSHARE PREPRINT OF CHAPTER 15 DOI: https://doi.org/10.6084/m9.figshare.34005519 FOR CONTACT AND AUTHOR'S WEBSITE DETAILS https://quantostatscomkhansitescrollytellingai.scrollytelling.ai