Quantum Mechanics: The Theoretical Minimum

This book fills an important gap between pop-sci and proper text books. It introduces QM with all the math without the robotic tone of text books. The book's writing style is conversational and I felt like I was sitting in Susskind's class. The book teaches the minimum necessary math to understand QM concepts which is very nice. I have other mathematical physics books that I have tried to learn QM math from and while those books are more rigorous they are also very boring and I tend to give up after reading few pages of those. This book always keeps it interesting. It took me two weeks of about 2-3 hours of study every day on week days and 5-6 hours on weekends days to finish this book. Unfortunately, I cannot give this book 5 stars because the book does not contain enough exercises. There are few exercises and many of those require proving some minor detail of the concept being explained. That is nice but if there's going to be only a few exercises I would rather have exercises that require me to apply the learned concept rather than proving some detail. This would be an amazing book if it had more easy-medium exercises. In fact last 3 chapters of the book where QM physics is discussed contains virtually no exercises at all. Susskind is a master at explaining difficult topics and he builds the concepts from ground up where very little is assumed which is very nice. Unfortunately, authors put very little effort in coming up with good exercises for practice. I still liked the book a lot though as now i feel prepared to tackle a proper text book such as Griffiths.

The book is very technical and requires a background in linear algebra and calculus. I was hoping for a explaination to the meaning behind the mathematical terms.

This book is designed to meet the needs of a mathematically inclined reader. An undergraduate level physics textbook is perhaps too advanced, and a popular book with no math discusses the principles of quantum reality that is easier to understand, but this book is at the middle level of complexity. This is meant for readers who are interested to know the equations that describes the mechanics of fundamental particles in terms of their position, motion, and energy in spacetime. Math tends to make certain things easy to put in perspective than mere descriptions without equations! The readers are expected to know mathematical concepts such as complex numbers, vector spaces, linear operators, and tensor products, all of which are artistically explained in a series of interludes. Specific concepts of the space of states, time evolution, principles of uncertainty, and quantum entanglement are described at moderate level of complexity, and yet reader-friendly. I recommend doing the exercises at the end of each chapter. I could not answer many of these questions, but it certainly makes you think. That is a learning process.

The biggest challenge is the understanding quantum entanglement because there is no classical analog for a system whose full state description contains no information about its individual parts, and nonlocality (two particles separated at large distances) is difficult to define. The best way to come to terms with these issues is to internalize the mathematics.

Two principles emerge as fundamental, the spin state of quantum particle or qubit. In classical physics, everything can be built out of yes/no (1 or 0) questions. Similarly, in quantum mechanics, every logical question becomes a question about qubits (basic unit of quantum information, two level quantum system, spin up or down, both in a state of superposition). The second principle is the harmonic oscillator. How do particles move in quantum mechanics? We know that fundamental particles have wave-particle duality. It exists in both wave and particle forms. Then how do matter in its wave state can have gravity associated with it? That makes understanding quantum gravity harder. In addition, waves oscillate much like a mass attached to the end of a spring. The oscillators, not masses attached to springs, are imagined as waves, in fact they are the oscillating electric and magnetic fields. For each wavelength, there is a mathematical harmonic oscillator describing the amplitude or strength of the field. For many waves there is a lot of harmonic oscillators all running simultaneously. Fortunately, they all oscillate independently. The higher-energy wave functions oscillate more rapidly and are more spread out. This is the consequence of quantum field theory. Another question is how do quantum states change with the evolution of time? They change so that information describing the system are never erased. This is one of the most fundamental phenomenon that haunts in describing black holes.

This book sticks to the simplest possible quantum system, one with a two-dimensional state space. The algebra is developed from scratch and author Leonard Susskind describes at a very leisurely pace and the quantum reality is described in the simplest context.

I wish I had read this during my first year of graduate school. It was probably a lot easier to get through now that I'm so familiar with the material, but it still helped me make a lot of new connections and it really influenced the way that I'll explain the concepts to others in the future. He covers the parts of quantum mechanics most relevant to quantum info and quantum computing too, in a very applicable way, which most other textbooks gloss over or touch on more abstractly. I'd recommend it to anyone who wants a better qm foundation, and I'd doubly recommend it to anyone who has a basic physics background and wants to see how to apply it to quantum information and quantum computing.