How to Learn Quantum

A Good Book: The Theory of Quantum Information or can be found in my local copy


From How to learn quantum mechanics on your own

Feynman Lectures on Physics, volume 3: Essential chapters: Chapter 1-12 (besides chapter 4 which is optional) I strongly recommend getting "Exercises for the Feynman Lectures on Physics" as well, and doing the problems. It's available online for fairly cheap (less than $20 USD).

Introduction to Linear Algebra by Gilbert Strang:

Also refer to 3b1b's linear algebra video

Quantum Mechanics - The Theoretical Minimum by Leonard Susskind and Art Friedman: you can find lecture on Youtube, but it is difficult to absorb its material without problem set.

A Modern Approach to Quantum Mechanics by Townsend: This book goes a bit further than you might need, so below are the essential chapters, along with how these chapters match up with those in The Theoretical Minimum

Advanced Topics

Quantum Computing: The one classic text for this is by Nielsen and Chuang. However, if you just want an overview, you might be better off with lecture notes that are available online, for example Mermin's excellent notes: http://www.lassp.cornell.edu/mermin/qcomp/CS483.html

Quantum Complexity Theory: This is quantum computing for a computer science perspective. Scott Aaronson has a great book on it, based on these lecture notes: https://www.scottaaronson.com/democritus/

Quantum Foundations: Decoherence and the quantum to classical transition by Schlosshauer is a wonderful book that helps explain why the world seems classical when it's actually quantum. He makes an excellent case for the Many Worlds interpretation along the way. It does get quite technical though, and a lot of the value is toward the beginning. So I think this article by the author covers a lot of the most salient points: https://arxiv.org/pdf/quant-ph/0312059.pdf

Quantum Field Theory: An interpretive introduction to quantum field theory by Teller is nothing like any normal QFT textbook. Instead of all being mathematics, he spends a lot of time on what it means.

Quantum Chemistry & Computational Chemistry: I've recently been reading about this because this is expected to be an area that quantum computing will really help with. I don't know anywhere near enough to recommend a textbook, but here's a nice review article: https://arxiv.org/pdf/1812.09976.pdf

Schrödinger Equation

Schrödinger Equation: where \hslash = \frac{h}{2\pi} is Plank's (revised) constant.

i\hslash = \frac{\partial \Psi}{\partial t} = - \frac{\hslash^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V\Psi

\Psi(x, t) is a complex number because otherwise the equation is imaginary.

\Psi(x, t) is a wave function that results a probability amplitude. Similar to Newton's second law, \Psi(x, t) determines the "location" of object in future time given \Psi(x, 0)

The statistical interpretation: |\Psi(x, t)|^2 is the probability density of finding particle at point x at time t.

\int_{-\infty}^\infty |\Psi(x, t)|^2 dx = 1
\int_a^b |\Psi(x, t)|^2 dx = \text{The probability of finding the particle between } a \text{ and } b \text{ at time } t

Philosophical Consequence of Schrödinger Equation

Suppose I measure the position of the particle at point x, we ask where as the particle just before I made the measurement.

Suppose I take another measurement immediately after the first measurement, would I get x as the result?

Solutions to Schrödinger Equation

Since Schrödinger Equation is a differential equation, if \Psi is a solution, then A\Psi is also a solution. So we impose the solution of Schrödinger Equation to sum to 1. This process is called normalization.

\int_{-\infty}^\infty |\Psi(x, t)|^2 dx = 1

However, for non-normalizable (non-square-integrable) solutions (where \Psi = 0 \lor \Psi = \pm \infty), the solution can't represent particles (not physically realizable states) and must be rejected.

Now, Schrödinger Equation has property such that if we find constant A that satisfy square-integrable along some specific time t, A can also be used for other time t.

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