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Selected Solved Problems in Quantum Mechanics

Kateřina Fišerová

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The main aim of this thesis was to create a set of problems in Quantum Mechanics, which would be included in a collection of solved problems in Physics available online on the website http://www.fyzikalniulohy.cz. As a result, thirty nine problems were completed, covering seven thematic areas partially of high school and mostly of introductory college Quantum Mechanics course. In general, the collection is mainly designed for college students as an exercise in basic quantum-mechanical problems and also for high school students, who have a desire to deal with some special problems. A detailed description of content, structure, and technical execution of this collection can be found in chapter 1 of this thesis. Another task was to review existing online collections of applets dealing with Quantum Mechanics. A selection of them is introduced in chapter 2 of this thesis.

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The main aim of this thesis was to create a set of problems in Quantum Mechanics, which would be included in a collection of solved problems in Physics available online on the website http://www.fyzikalniulohy.cz. As a result, thirty nine problems were completed, covering seven thematic areas partially of high school and mostly of introductory college Quantum Mechanics course. In general, the collection is mainly designed for college students as an exercise in basic quantum-mechanical problems and also for high school students, who have a desire to deal with some special problems. A detailed description of content, structure, and technical execution of this collection can be found in chapter 1 of this thesis. Another task was to review existing online collections of applets dealing with Quantum Mechanics. A selection of them is introduced in chapter 2 of this thesis.
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
This bachelor thesis deals with the creation of a Czech didactic text for teaching quantum algorithms at high schools. The thesis describes five basic quantum algorithms, namely Deutsch's, Deutsch-Jozsa, Bernstein-Vazirani, Simon's, and Grover's, which uti- lize a quantum oracle and form a theoretical foundation for more complex quantum algorithms. The theoretical explanation is supplemented with motivational and illustra- tive examples. The individual procedures are elaborated in such a way that the text is fully comprehensible to students at an upper secondary school level of knowledge. To facilitate orientation in the subject matter, an introductory chapter was created, summa- rizing the reader's expected knowledge and the necessary mathematical apparatus. The thesis concludes with a chapter providing a comprehensive summary of all the described algorithms.
This book contains more than 300 problems in quantum mechanics with accompanying solutions, covering topics that are commonly taught in first-year graduate physics programs. Special care is given to each problem's formulation, with detailed and extensive solutions provided to support understanding. The problems span a range of difficulties, from basic exercises to more challenging applications and extensions of the standard material. Students are required to think critically and incorporate physics and mathematical techniques learned previously or concurrently to solve the more challenging problems. Each chapter begins by framing the particular topic being examined with a short theory section that sets the context for and motivates the problems that follow. This text is well suited for self-study or as a useful supplement to the existing quantum mechanics textbooks for upper-undergraduate and graduate students, and their instructors.
This helpful and pedagogical book offers problems and solutions in quantum mechanics from areas of current research, rarely addressed in introductory courses or textbooks. It is based on the authors' own experience of teaching undergraduate and graduate courses in quantum mechanics, and adapts problems from contemporary research publications to be accessible to students. Each section introduces key quantum mechanical concepts, which are followed by exercises that grow progressively more challenging throughout the chapter. The step-by-step solutions provide detailed mathematical derivations, and explore their application to wider research topics. This is an indispensable resource for undergraduate and graduate students alike, expanding the range of topics usually covered in the classroom, as well as for instructors and early-career researchers in quantum mechanics, quantum computation and communication, and quantum information.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
This book is particularly designed for the undergraduate and post graduate level students, specially beginners of quantum mechanics, of Indian as well as foreign universities.The book begins with a firm grounding in the basics of quantum mechanics.Special effort is given to emphasize things by providing sufficient numerical exposure to the students. Rich selection of problems and their simple solutions in every chapter, is bound to give the students a firm grip on the topic. Apart from those, formulas for numerical problems are highlighted properly to help the students to select them efficiently whenever necessary. In between every chapter, a large number of unsolved problems with due hints are given so that the readers can apply the underlying principles in solving these problems.Conceived mainly for graduate/post graduate students, this book will also be helpful for all, who wish to acquire some knowledge of quantum mechanics.