Book Reviewed: Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman

Learning quantum mechanics from a maestro 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.