دانلود کتاب مکانیک کوانتومی ابتدایی – با مسائل و راه حل ها

This book has grown out of a one term course on quantum mechanics in the School of Mathematics at the University of Bristol. I have taught this course several times, but this book benefits immensely from the previous notes of Martin Sieber, Noah Linden, and Toby Cubitt. I am grateful that they have shared their materials with me. There is an extensive set of problems and solutions for this book. Many of the problems are my own, and some I have used in exams for the course. I have undoubtedly been influenced in my choice of problems by my own past courses in quantum mechanics, and some of those sources are mentioned in the book, The book is intended for mathematics undergraduates. Generally, this means that the students do not have the background in physics to appreciate the issues surrounding the origin and development of quantum mechanics. One point that I try to emphasize is how new mathematics had to be developed in parallel with the quantum physics. In fact, ”quantum mechanical thinking” has had a tremendous influence on mathematical thinking. A recent example of this is the fascinating review paper on linear stability analysis in fluid mechanics.1 I hope that this tempts the students to study much of the physical background on their own with the supplemental references at the appropriate level that I give. Concerning prerequisites, I have tried to make the book as self-contained as possible. The amount of linear algebra required is not much beyond the level of computing the eigenvalues and eigenvectors of 2×2 matrices (with complex entries). The Schr¨odinger equation is a linear partial differential equation but I only consider potential energy functions that are independent of time. Therefore it can be analyzed using separation of variables. This is done once, and the necessary background can be developed in the context of this calculation. Consequently, only simple linear ordinary differential equations are required, which almost all students have seen before. I have taught this course in both the UK and the US to second, third, and fourth year mathematics students and prerequisites have not been an issue. In my experience, the material in this book can be covered in twelve weeks. While this book originated during my time in the city of Bristol, United Kingdom, I have completed it in the past few months during my stay at the United States Naval Academy in Annapolis, Maryland. During this time I have used the book in teaching the course SM421, Elementary Quantum Mechanics, which was attended by third and fourth year students in mathematics. That class of midshipmen, Angela Feng, Nico Gonzalez- Reed, Jack Judy, Gabe Kitsch, James McAtee, Ivette Ayala, Cohen Bruner, Luke Gasper, Maya Kessner, Emily Rose Kosanovich, George Main, Will Nguyen, and Teagan Flinn, were particularly inquisitive and helpful in asking questions and I am grateful for all of their input and lively class participation. Spring of 2024 was a particularly challenging time for me and I am very grateful to Prof Kevin McIlhany of the department of physics at the Naval Academy for covering my lectures in the latter half of the course.