Quantum Mechanics for Beginners

2020 ◽  
Author(s):  
M. Suhail Zubairy
Keyword(s):  
High School ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Communication ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Superposition ◽  
Quantum Dense Coding ◽  
Foundation Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
And Mathematics

Quantum mechanics is a highly successful yet a mysterious theory. Quantum Mechanics for Beginners provides an introduction of this fascinating subject to someone with only a high school background in physics and mathematics. This book, except the last chapter on the Schrödinger equation, is entirely algebra-based. A major strength of this book is that, in addition to the foundation of quantum mechanics, it provides an introduction to the fields of quantum communication and quantum computing. The topics covered include wave–particle duality, the Heisenberg uncertainty relation, Bohr’s principle of complementarity, quantum superposition and entanglement, Schrödinger’s cat, Einstein–Podolsky–Rosen paradox, Bell theorem, quantum no-cloning theorem and quantum copying, quantum eraser and delayed choice, quantum teleportation, quantum key distribution protocols such as BB-84 and B-92, counterfactual communication, quantum money, quantum Fourier transform, quantum computing protocols including Shor and Grover algorithms, quantum dense coding, and quantum tunneling. All these topics and more are explained fully but using only elementary mathematics. Each chapter is followed by a short list of references and some exercises. This book is meant for an advanced high school student and a beginning college student and can be used as a text for a one semester course at the undergraduate level. However it can also be a useful and accessible book for those who are not familiar but want to learn some of the fascinating recent and ongoing developments in areas related to the foundations of quantum mechanics and its applications to quantum communication and quantum computing.

No-cloning Theorem and Quantum Copying

2020 ◽  
pp. 172-181
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Uncertainty Relation ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Cloning ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Copying ◽  
Arbitrary Quantum ◽  
Principle Of Complementarity

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

Mathematical Foundations of Quantum Mechanics

2018 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Foundations Of Quantum Mechanics ◽  
Theoretical Physics ◽  
Mathematical Framework ◽  
Von Neumann ◽  
New Science ◽  
Freeman Dyson ◽  
And Mathematics ◽  
Mathematical Foundations ◽  
First Time

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.

scholarly journals Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function

2021 ◽  
Author(s):  
Shuming Wen
Keyword(s):  
Quantum Mechanics ◽  
The State ◽  
Particle State ◽  
State Function ◽  
Quantum Superposition ◽  
Wave State ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Tunnelling ◽  
Wave Particle Duality ◽  
Objective System

Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the state function of a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, We find that the state function of the particle has precise physical meaning; that is, the particle periodically and alternately exhibits the particle state and wave state in time and space, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.

scholarly journals Tripartite Entanglement: Foundations and Applications

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 209 ◽  
Author(s):  
Márcio M. Cunha ◽  
Alejandro Fonseca ◽  
Edilberto O. Silva
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Essential Role ◽  
Quantum Information Processing ◽  
Foundations Of Quantum Mechanics ◽  
Discrete Variables ◽  
Tripartite Entanglement ◽  
W States ◽  
Quantum Protocols ◽  
Bipartite Case

We review some current ideas of tripartite entanglement. In particular, we consider the case representing the next level of complexity beyond the simplest (though far from trivial) one, namely the bipartite case. This kind of entanglement plays an essential role in understanding the foundations of quantum mechanics. It also allows for implementing several applications in the fields of quantum information processing and quantum computing. In this paper, we review the fundamental aspects of tripartite entanglement focusing on Greenberger–Horne–Zeilinger and W states for discrete variables. We discuss the possibility of using it as a resource to execute quantum protocols and present some examples in detail.

scholarly journals How Quantum is Quantum Counterfactual Communication?

2021 ◽  
Vol 51 (1) ◽  
Author(s):  
Jonte R. Hance ◽  
James Ladyman ◽  
John Rarity
Keyword(s):  
Quantum Mechanics ◽  
Energy Transfer ◽  
Quantum Physics ◽  
Foundations Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
Insight Into ◽  
Matter Energy

AbstractQuantum Counterfactual Communication is the recently-proposed idea of using quantum physics to send messages between two parties, without any matter/energy transfer associated with the bits sent. While this has excited massive interest, both for potential ‘unhackable’ communication, and insight into the foundations of quantum mechanics, it has been asked whether this process is essentially quantum, or could be performed classically. We examine counterfactual communication, both classical and quantum, and show that the protocols proposed so far for sending signals that don’t involve matter/energy transfer associated with the bits sent must be quantum, insofar as they require wave-particle duality.

THE DEVELOPMENT OF ALGORITHMIC CULTURE AND PROGRAMMING CULTURE OF STUDENTS IN PROFILE CLASSES WHILE STUDING THE BASIS OF PROGRAMMING IN C++

2020 ◽  
pp. 24-33
Author(s):  
K. V. Rozov
Keyword(s):  
High School ◽  
High School Students ◽  
Educational Process ◽  
Writing Programs ◽  
School Students ◽  
Knowledge And Skills ◽  
C Programming ◽  
And Mathematics ◽  
Basic Level ◽  
Special Control

The article presents the structure, content and results of approbation of the C++ programming course developed for the 10th grade students of physics and mathematics profile and implemented as part of the academic subject “Informatics”. The aim of the course is to develop in the student not only knowledge and skills in programming, but also his algorithmic culture and programming culture as important qualities of a potential IT-specialist. This is facilitated by special control of educational process by the teacher, which consists in monitoring the activities of students in writing programs and timely correction of this activity. The assessment of the level of development of student algorithmic culture and programming culture relative to the basic level of their formation (when mastering the basics of algorithmization and programming in the 9th grade) was carried out on the basis of a number of criteria presented in the article. The results of approbation showed that the specially organized teacher activity makes it possible to increase the level of algorithmic culture and programming culture of high school students when studying the basics of programming in C++.

Students graduate of the degree course in Natural Sciences and Mathematics and the exercise of teaching profession: findings and implications for basic education

2020 ◽  
Vol 13 (2) ◽  
pp. 51
Author(s):  
A. C. R. Trevisan ◽  
E. P. Trevisan
Keyword(s):  
High School ◽  
Decision Making ◽  
Basic Education ◽  
Natural Sciences ◽  
Teaching Profession ◽  
Decision Making Process ◽  
Teaching Career ◽  
Professional Performance ◽  
Current Scenario ◽  
And Mathematics

In the article we seek to address questions regarding the interest of graduates of a degree course in Natural Sciences and Mathematics in relation to the teaching career in basic education. The course enables its graduates to work in the subjects Science and Mathematics in the final years of elementary school and Mathematics, Physics and Chemistry in high school. Our intention is to identify and reflect on the perceptions of these graduates about teaching, highlighting with this inherent aspects to the exercise of this profession in basic education. From the application of questionnaires to graduates of this course, we produced data regarding their performance in basic education, which enabled us to reflect on the national scenario in relation to the exercise of this profession. We could observe that the majority of the students participating in the research are not working in basic education and that the current scenario of devaluation of the teaching career exerts a significant influence in the decision making process of choosing or not the teacher profession for professional performance after graduation.

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