Category Archives: Quantum Mechanics

Quantum Theory and Representation Theory, the Book

For the last few years most of my time has been spent working on writing a textbook, with the current title Quantum Theory, Groups and Representations: An Introduction. The book is based on a year-long course that I’ve taught twice, … Continue reading

Posted in Quantum Mechanics | 13 Comments

The Free Particle

Following on my notes about Euler’s formula, I’ve finally finished some work on another piece of elementary exposition, a discussion of the free quantum particle, which can be found as chapters 10, 11 and 12 of the book I’m working … Continue reading

Posted in Quantum Mechanics | 19 Comments

The West Coast Metric is the Wrong One

I’m trying to get back to blogging about quantum mechanics slogans, this one is about relativistic quantum mechanics. I’m hoping it will stir up more trouble than my last East vs. West one. If you’re doing calculations in relativistic quantum … Continue reading

Posted in Quantum Mechanics | 61 Comments

This Week’s Hype

From commenter Hendrik, there’s the news that USC has put out a press release claiming that String Theory Could Be the Foundation of Quantum Mechanics. These claims are based on this paper, which argues that finding the Heisenberg commutation relations … Continue reading

Posted in Quantum Mechanics, This Week's Hype | 5 Comments

Use the Moment Map, not Noether’s Theorem

For a fourth provocative slogan about quantum mechanics I’ve chosen: Use the moment map, not Noether’s Theorem. Pretty much every physics textbook these days explains the way symmetry principles work as: Start with an action functional, invariant under a Lie … Continue reading

Posted in Quantum Mechanics | 25 Comments

Nature is Fundamentally Conformally Invariant

For a third slogan I’ve chosen: Nature is fundamentally conformally invariant. Note the weasel-word “fundamentally”. We know that nature is not conformally invariant, but the kind of thing I have in mind is pure QCD, where the underlying classical theory … Continue reading

Posted in Quantum Mechanics | 33 Comments

Grand Unification of Mathematics and Physics

For a second slogan about quantum mechanics I’ve chosen: Quantum mechanics is evidence of a grand unification of mathematics and physics. I’m not sure whether this slogan is likely to annoy physicists or mathematicians more, but in any case Edward … Continue reading

Posted in Quantum Mechanics, Uncategorized | 7 Comments

Quantum Theory is Representation Theory

For a first slogan (see here for slogan zero) I’ve chosen: Quantum theory is representation theory. One aspect of what I’m referring to is explained in detail in chapter 14 of these notes. Whenever you have a classical phase space … Continue reading

Posted in Quantum Mechanics | 43 Comments

What’s Hard to Understand is Classical Mechanics, Not Quantum Mechanics

For a zeroth slogan about quantum mechanics, I’ve chosen What’s hard to understand is classical mechanics, not quantum mechanics. The slogan is labeled by zero because it’s preliminary to what I’ve been writing about here. It explains why I don’t … Continue reading

Posted in Quantum Mechanics | 46 Comments

Fall QM Course

This year I’ll be teaching a new version of the same course on quantum mechanics aimed at mathematicians that I taught during the 2012-3 academic year (there’s a web-page here). During the last course I started writing up notes, and … Continue reading

Posted in Quantum Mechanics | 8 Comments