Tuesday, April 21, 2015

"Quirky Quantum Concepts" by Eric L. Michelsen

You've taken a first course in quantum mechanics. You know your way round Schrödinger’s equation, eigenstates and eigenvalues, and you've thoroughly explored the hydrogen atom. But deep down you’re confused.

You read about Schrödinger’s Cat and that you don’t see superpositions ‘in real life’ because of ‘decoherence’, but what’s that? Populist accounts talk airily about the 'leakage of phase information into the environment', but that sort of hand-waving hardly adds clarity. The technical literature discusses the exponential decay of off-diagonal terms in the density matrix ... but what’s physically going on?

You read about the various interpretations. Is the wave function part of reality? Is it just a subjective statement of the experimenter’s state of knowledge? So much ink discussing the significance of Schrödinger’s equation: and of course, that eponymous equation isn't even correct. The road to the truth about quantum mechanics must run through its relativistic cousin, quantum field theory. But what a chasm separates you, the student, from that towering intellectual achievement. No-one can explain in accessible terms what QFT is, the map of the territory. Saying baldly that 'at each point in space and time there are an infinite number of simple harmonic oscillator modes (with creation and annihilation operators) for each type of fundamental particle'  ... doesn't really do it for most people.

What you need is a book in which these concepts are discussed via simple models, mathematically clear but at a level accessible to people who've completed a first course in quantum mechanics at undergraduate level (and understood it). Eric Michelsen has admirably succeeded in this book, which is a natural successor to Gary Bowman’s Essential Quantum Mechanics. In both cases the texts are meant to be read alongside a traditional textbook, but focus on conceptual clarity – what is the maths really saying? – and a careful linkage with what’s observed in reality.

Quirky Quantum Concepts covers many other topics.  There are fine reviews of wave mechanics itself; scattering (barely touched on in most elementary classes); matrix mechanics and density matrices; angular momentum; and the QM treatment of multi-electron atoms. But for me the clear treatment of loss of coherence and the very introductory but rigorous and comprehensible guide to QED/QFT were the high points of this excellent book.

(Note: as a bonus, the PDF is available on the Internet. I bought the book not just through guilt – it’s easier to flip to and fro in hard copy).