On Some of Physics’ Problems

Eugene Paul Wigner

Jaroslav Kafka

Title: Solved Problems in Quantum Physics - angular momentum and spin Author: Jaroslav Kafka Department: Department of Physics Education Supervisor: RNDr. Zdeňka Koupilová, Ph.D., Department of Physics Education Abstract: The aim of this bachelor thesis was to create a set of solved problems in quantum physics for the electronic Collection of Solved Problems in Physics. Within this thesis 18 problems were created, which belong to the chapter Microworld Physics, mostly at the undergraduate level. There is described a brief history of the electronic collection and its technical background in the context of the user and the administrator. Part of the thesis includes description of the tasks in the matter of physical issues and its interconnection with other tasks of the Collection of Solved Problems in Physics. In the appendix there are presented selected solved problems with structured sollution. All tasks can be found on the website http://reseneulohy.cz/ or on the attached CD. Keywords: electronic collection, solved problems, quantum physics 1

W. Macdonald Smith

Овчинников С. В.

The relevance of the research is determined by the fundamental nature of the P vs NP problem, which has been considered a central unsolved problem in theoretical computer science for more than half a century. In this article, for the first time, it is proved that the problem of solving the P vs NP problem is not a mathematical problem, but a physical problem, the solution of which depends on the physical implementation of the computing system. The aim of this paper is to prove that the solution of the P vs NP problem depends on the type of physical system used for calculations. The leading approach to research is to synthesize three independent paradigms: 1. Algebraic topology that provides invariants for complexity classification. 2. Quantum physics, which provides parallel information processing. 3. Apparat implementation on the GPU that demonstrates the physical limitations of classical computing. Author's results include: A formal proof that P ≠ NP holds in classical physics (Newtonian mechanics, deterministic computations) and a simultaneous proof that P = NP holds in quantum physics (superposition, entanglement). Experimental confirmation of the physical implementation through a series of computational experiments. Development of hybrid system that allows you to switch between modes depending on the available resources. The theoretical significance lies in rethinking the fundamental problem of complexity theory as a physical law. Practical significance is the creation of an adaptive computing system, the efficiency of which is determined by the available physical platform.

Vishwamittar

Z. Ficek

This book contains tutorial problems with solutions for the textbook Quantum Physics for Beginners. The reader studying the abstract field of quantum physics needs to solve plenty of practical, especially quantitative, problems. This book places emphasis on basic problems of quantum physics together with some instructive, simulating, and useful applications. A considerable range of complexity is presented by these problems, and not too many of them can be solved using formulas alone.