No-Nonsense Quantum Mechanics: A Student-Friendly Introduction, Second Edition

Book Preface

Quantum mechanics is nearly a century old and hundreds of books on the subject have already been written. Despite the sheer volume of material on the subject, quantum mechanics unfortunately remains a challenging subject to learn.
When I first learned quantum mechanics, I remember being utterly lost. I struggled for months to understand even the easiest concepts.  In some sense, this is entirely normal. For example, you may be familiar with the famous quote usually attributed to Niels Bohr: “If you are not completely confused by quantum mechanics, you do not understand it.” This sentiment is echoed by Roger Penrose, who explained that his “general attitude” to quantum mechanics is that “it makes absolutely no sense!”
It follows that learning quantum mechanics is necessarily diffi­cult and confusing, right?
I no longer believe this to be true. This change of heart served as my motivation to write this book.
To be clear: quantum mechanics is not an easy subject. It takes some time to get used to. You need to learn a completely new formalism. However, this new formalism is not as difficult as most authors would lead you to believe; you don’t need to spend months in a state of confusion. Also, rest reassured that my goal is not to promote some crackpot alternative to quan­tum mechanics in order to remove all = “quantum paradoxes” and “quantum mysteries”. Instead, a large part of this book is devoted to topics which are covered by most other = textbooks. However, my goal is to introduce them as gently as possible and, in some sense, I wrote the book I wished had existed when I started learning quantum mechanics.

So what exactly makes this book different?

– First, it wasn’t written by a professor. As a result, this book is by no means an authoritative reference. Instead, this book is written more like a casual conversation with a more expe­rienced student who shares with you everything he wished he had known earlier. I’m convinced that someone who has recently learned the topic can explain it much better than someone who learned it decades ago. Many textbooks are hard to understand, not because the subject is difficult, but because the author can’t remember what it’s like to be a be­ginner1 .

– Second, this book focuses solely on the fundamentals and contains no fluff. Most other books on quantum mechanics bury the essential concepts behind tedious calculations and complicated formulas.

– Third, this book is unique in that it contains lots of idiosyn­ cratic hand-drawn illustrations. Usually, textbooks include very few pictures since drawing them is either a lot of work or expensive. However, drawing figures is only a lot of work if you are a perfectionist. The images in this book are not as pretty as the pictures in a typical textbook since I firmly be­lieve that lots of non-perfect illustrations are much better than a few perfect ones. The goal of this book, after all, is to help you understand quantum mechanics and not to win prizes for my pretty illustrations.

– Finally, my only goal was to write the most student-friendly quantum mechanics book and not, for example, to build my reputation. Too many books are unnecessarily complicated because if a book is hard to understand, it makes the author appear smarter.2 To give a concrete example, nothing in this book is assumed to be “obvious” or “easy to see”. Moreover, calculations are done step-by-step and are annotated to help you understand faster.

With that said, the actual content and structure of the book is also somewhat non-standard:
In the first part, we will talk about the essential features of quantum mechanics and how we can describe them mathemat­ically. We start with a “Bird’s Eye View” of quantum mechanics and then gradually refine our understanding.
Afterwards, we will discuss concrete examples and applica­tions. We will stick to the most fundamental examples that show how quantum mechanics works in practice. In most more advanced examples, we don’t learn anything new. Instead, the same lessons are buried behind more complicated calculations. I will, however, comment on several important advanced exam­ples with which you should become familiar. Next, we will talk about alternative formulations of quantum mechanics) Most other textbooks focus solely on the wave function formulation and ignore the alternatives. However, just as it is worthwhile to learn both the Lagrangian and Hamilto­nian formulations of classical mechanics, learning these alterna­tive formulations can be extremely beneficial. This is especially true when we try to understand what quantum mechanics really means, which is the topic of the penultimate chapter.
In the final chapter, we will discuss where you can learn more depending on what aspect of quantum mechanics interests you the most.  So, without any further ado, let’s begin. I hope you enjoy read­ing this book as much as I have enjoyed writing it.