Quantum Mechanics Barton Zwiebach

[Rebbeca Schulke]

Part 1, on essentials, offers a sound introduction to the subject, touching on such topics as states and probability amplitudes, the Schrdinger equation, energy eigenstates of particles in potentials, the hydrogen atom, and spin one-half particles. Part 2, on theoretical foundations, covers mathematical tools, the pictures of quantum mechanics and the axioms of quantum mechanics, entanglement and tensor products, angular momentum, and identical particles. Part 3, on applications, introduces tools and techniques that help students master the theoretical concepts with a focus on approximation methods. About 240 exercises appear throughout the text, and nearly 300 end-of-chapter problems support the understanding of the subject. After mastering the material in this book, students will have the strong foundation in quantum mechanics that is required for graduate work in physics.

I have finished the Quantum Mechanics: Beginner to Expert course on Udemy. After finishing it, I felt like I'm an expert at QM and went to PSE to answer someone's question. It's pretty obvious what happened next. So what else should I learn so my knowledge/understanding of QM is complete?

Congrats on finishing that course. If you like video courses you could consider following MIT's Quantum Physics I, II, and/or III. I've watched hours of these and Barton Zwiebach is a great teacher. Each video description on YouTube also has a link to exercises assigned at MIT for that course. Here are links to the three courses:

Some of that content will have been covered in the first course you took and some not, according to the description I see of the course you linked. You would have to outline the MIT content and choose which of it is new to you. The courses are real Quantum Mechanics courses at MIT.

I'd like to refer you to one more source if you want to understand quantum mechanics from its foundations up, which is Shankar's Principles of Quantum Mechanics. It is one of the most common graduate-level Quantum Mechanics textbooks. It is not too hard to find a PDF online. You could use it as a reference on the side with the MIT course. The most important chapters here are chapters 1 and 4.

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This undergraduate textbook offers a comprehensive overview of quantum mechanics, beginning with essential concepts and results, proceeding through the theoretical foundations that provide the field's conceptual framework, and concluding with the tools and applications students will need for advanced studies and for research. Drawn from lectures created for MIT undergraduates and for the popular MITx online course, "Mastering Quantum Mechanics," the text presents the material in a modern and approachable manner while still including the traditional topics necessary for a well-rounded understanding of the subject. As the book progresses, the treatment gradually increases in difficulty, matching students' increasingly sophisticated understanding of the material. - Part 1 covers states and probability amplitudes, the Schrdinger equation, energy eigenstates of particles in potentials, the hydrogen atom, and spin one-half particles
- Part 2 covers mathematical tools, the pictures of quantum mechanics and the axioms of quantum mechanics, entanglement and tensor products, angular momentum, and identical particles.
- Part 3 introduces tools and techniques that help students master the theoretical concepts with a focus on approximation methods.
- 236 exercises and 286 end-of-chapter problems
- 248 figures

"A First Course in String Theory" is a comprehensive introduction to the fundamental concepts and principles of string theory, a theoretical framework that attempts to unify all forces of nature, including gravity. The book covers topics such as classical and quantum mechanics, relativity, and modern particle physics, and provides a solid foundation for further exploration of string theory.

Barton Zwiebach is a renowned physicist and professor at the Massachusetts Institute of Technology (MIT). He is an expert in string theory and has made significant contributions to the field. He is also a recipient of numerous awards and honors for his research and teaching, making him highly qualified to write about string theory.

Yes, "A First Course in String Theory" is written for undergraduate and graduate students with a basic understanding of physics and mathematics. The book starts with an overview of classical mechanics and gradually introduces more advanced concepts, making it accessible to beginners.

One of the main strengths of "A First Course in String Theory" is its clear and concise presentation of complex concepts. The book also includes numerous examples and exercises to help readers better understand the material. Additionally, it covers a wide range of topics, from the basics of string theory to advanced topics like black holes and cosmology.

Yes, "A First Course in String Theory" can be used as a reference book for those already familiar with the basics of string theory. The book is well-organized, with a comprehensive index and a summary of key equations at the end of each chapter, making it a useful resource for students and researchers alike.

If you are planning to enter a graduate program in physics in the US, it is fairly certain you will (if you haven't already) hear horror stories about John David Jackson's canonical graduate electrodynamics textbook (simply referred to as "Jackson"). To me, and decades of physicists that have come before me, Jackson is the archetype of a graduate textbook: exact and comprehensive, but extremely challenging to learn from. Many graduate texts, in general, focus on rigor and completeness at the expense of pedagogy. Perhaps this would be okay, if an expert researcher in a relevant field was the professor and helped the students understand the text throughout the course. Sadly, all-too-often, the aforementioned expert researcher is largely unable to communicate effectively to the novice student. So, if lectures don't seem to help and self-study is intractable, where should one turn? How, under these circumstances, could one hope to succeed in graduate school? The answer is simple: having several high quality supplemental resources is absolutely crucial for success in graduate school.

Thus, in this post I hope to construct just such a list for the courses which are almost always required in US physics graduate programs. Namely, I will suggest resources for: classical mechanics, quantum mechanics, electromagnetism, and statistical mechanics. I hope this list will benefit both struggling graduate students as well as motivated undergraduates that want to prepare for graduate studies. Personally, I find lengthy lists of resources somewhat overwhelming. The list that follows is not meant to be comprehensive, but rather contains many of the resources I used to get through the core courses at the University of Colorado, Boulder. Within each subsection, I attempt to order the resources by difficulty (from most accessible to least). Further, I will attempt to qualify each one when necessary. In general, though, they are all great and I hope you find them as useful as I did.

Although surely not as "hip" as it was when Newton dropped the Principia back in 1687, classical mechanics ("class mech" for short) is an essential part of a graduate physics education. The fairly standard graduate text is by Goldstein and it can, compared to introductory courses on the subject, feel needlessly mathematical. In fact, a lot of graudate physics courses felt more like mathematical hazing than physics education to me. With that said, here are a few resources that helped me all the way through to the comprehensive physics exam.

If I could tell high school me one thing that would help him excel in physics, it would be to relentlessly study abstract linear algebra. I continue to be surprised by how ubiquitously useful linear algebra is throughout physics. In some places, it is extremely useful, in graduate QM, it is absolutely essential.

1. Grant Sanderson's Essence of Linear Algebra Series: If you do not know 3blue1brown on YouTube, I cannot more highly recommend them. Their videos remind me why I love math and education. Specifically, his linear algebra series is a great visual overview of the subject.

• Sheldon Axler's Linear Algebra Done Right : The title says it all. If you understand this book cover to cover, you'll be (arguably) over-prepared for graduate QM. I was extremely excited when I stumbled upon several lectures from Axler's book by my favorite professor: Barton Zwiebach at MIT. If you are looking for a serious linear algebra crash course before starting graduate QM, Barton's lectures on linear algebra are the place to start.

Here, I will group all of the recommendations together because my feel for what is and is not at the graduate level is far less well-defined for electromagnetism. Nonetheless, I will rank them from most accessible to least. Keep in mind, of course, that accessibility is a function of one's educational background. Just because someone says something is "supposed to be easy," doesn't mean it is. Such language is at best slightly helpful and at worst needlessly harmful.

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