Ch. 1: On interpretations
The biggest impediment to understanding quantum mechanics is having nothing to visualize because the predominant philosophy in quantum mechanics is anti-reality and tells us not to ask questions about what actually exists. With this chapter, I lay bare part of the shaky foundation of the predominant philosophy because I want to dispel the idea that you are not allowed to think of what happens in the quantum realm. I’m not fond of rehashing the history you’ve read a few times in other pop-sci accounts, but in this chapter, we must go back in time and see the arguments of a most influential physicist who thought himself a great philosopher.
Ch.2: A first look at quantum angular momentum
You are undoubtedly aware of spin angular momentum (spin) but may be unaware of its counterpart, orbital angular momentum (OAM). Together, they are the two types of quantum angular momentum (QAM). QAM will be one of the most difficult topics to comprehend in this book, so I lay out how you should mentally picture these concepts in this chapter.
Ch. 3: Misconceptions about the electron in particular
Some illogical and naive ideas are out there that picture quantum objects as tiny, corpuscular particles or as geometric points. They usually come up in discussions that include electrons. These naive ideas stop many from appreciating that the wave function is the center of it all. I show why the pictures are illogical and introduce how to think of the state of a particle.
Ch. 4: Waves and superposition
Mathematically, superposition is a simple idea. It is the addition of fields of numbers. This short chapter gives you some insight into how to understand superpositions mathematically and physically.
Ch. 5: The cat, the keg, and the cut
This is the second and final chapter with a significant call back to history. Pop-sci authors and click-bait websites are fond of mischaracterizing what Schrödinger said about his cat experiment. I correct the record on this and also give Einstein’s version of the cat experiment. At this point in history, the physicist-philosopher of the first chapter wanted to defend his Copenhagen interpretation from criticisms by Einstein and Schrödinger, so I have a go at another aspect of his anti-realist claims. I end with an exploration of the idea of macroscopic wave functions.
Ch. 6: Mathematics vs. measurements
This is where a gentle introduction to using Dirac’s mathematical notation of kets, operators, and numerical quantities begins. I use it to show you that some claims from the mathematics of quantum mechanics do not match the physical situation that occurs in actual experiments.
Ch. 7: Wave-particle duality and the double-slit experiment
The term wave-particle duality is so abused that I must give a critical analysis of it. Most explanations of the double-slit experiment make it seem like quantum mechanics is magical. I walk through a description of the double-slit experiment by a British professor and show you how it misleads you into thinking that quantum objects behave magically.
Ch. 8 and 9: The mysterious hieroglyphics of Schrödinger’s equation
On a few occasions, you have probably been presented with the mass of symbols that is the Schrödinger equation. Yet, it still seems undecipherable. I take two chapters to show you what the math means, first As an energy balance and then As a wave equation.
Ch. 10: Gallery of atomic orbitals
The Schrödinger equation gives us the wave functions for hydrogen’s atomic orbitals. Via dozens of colorful images, I examine the matter density of hydrogen and the complex-valued nature of its wave functions.
Ch. 11: Spins, superpositions, and abstract spaces
Spin and superpositions are two of the topics that novices find particularly counterintuitive. I give a comprehensive explanation of spin and its superpositions to give you a definitive account of how you should view things. I also use abstract mathematical spaces to illustrate why spins and superpositions are so counterintuitive. To give you a more complete understanding, I do not restrict myself to spin-1/2 states. I end the chapter with examples of spin-0, spin-1, and spin-3/2 states.
Ch. 12: Spring cleaning
Some misconceptions I must dispose of are delayed until this chapter because you need the foundational concepts from previous chapters. In order to accomplish this spring cleaning, you also meet the final three postulates here.
Ch. 13: The uncertainty principle is not what you think it is
Far too often, the uncertainty principle is confused with a measurement process or is used to justify fantastical stories of a frantic quantum realm. In this chapter, I show you what the uncertainty principle is fundamentally about, and it’s certainly not measurements.
Ch. 14: The postulates of quantum mechanics
Often, students are told we have an axiomatic system of quantum mechanics, which should mean unerring truths follow from a foundational set of postulates. Throughout the book, I have pointed out where some of these postulates don’t work as universally as they are claimed to. In this chapter, I teach you what it means to have an axiomatic system and give an extensive commentary on the postulates and what goes unsaid.
Afterword
A few parting words to give you some direction.
Appendix A: Atomic orbitals, their labels and transitions
This appendix teaches you the numbering and lettering system for orbitals. It also explains the types of quantum states and gives a cursory explanation of atomic transitions. Before starting the \emph{Gallery of atomic orbitals} chapter, you should understand this labeling system.
Appendix B: The postulates of quantum mechanics, a non-mathematical overview
I pepper introductions to ten postulates across various chapters. You should often refer to the alternative wording in this appendix to keep the ideas straight in your mind.
Appendix C: Matrix mechanics and spin
At various points in the book, I presented some spin superpositions and expectation values and promised to show you how these and some other math objects came about. I keep my promise with this appendix. It is for those who want a peek into a small subset of the math of matrix mechanics hidden behind Dirac’s notation.
Appendix D: The energy-time uncertainty principle doesn’t exist
It is important to know that the so-called energy-time uncertainty principle cannot be rigorously derived from quantum mechanics. I illustrate that to you with this appendix.
Glossary
A comprehensive glossary with detailed entries. Sometimes I explain a concept differently here, so the reader should refer to the glossary often. After finishing a chapter, I suggest reviewing the chapter’s important terms here.
Bibliography & Index
You know what these are.