Thursday, October 08, 2009

Open University: SM358 The Quantum World

This third level OU physics course comes in three books.

Book 1: wave mechanics introduces Schrödinger’s equation and takes the reader through the standard models of particles in infinite and finite square wells, simple harmonic oscillators, and free particle wave packets. The book concludes with a first look at scattering and tunnelling, along with probability currents.

Book 2: quantum mechanics and its interpretation starts with Dirac notation and the vector space model of quantum states. The next few chapters introduce the angular momentum operators and spin followed by many-particle systems and indistinguishability, including the Pauli exclusion principle.

The final part of the book moves into the modern areas of quantum entanglement and the EPR ‘paradox, and briefly introduces quantum cryptography, quantum teleportation and a very brief mention of quantum computing.

Book 3: quantum mechanics of matter opens with a thorough analysis of the hydrogen atom. We start with spherical harmonics, then look at the radial equation (for the radial part of the wave function in spherical coordinates). This allows us to account for the spectroscopic data for hydrogen in a first approximation.

In chapter 3 we detour to study perturbation methods for solving more complex versions of the Schrödinger equation by approximation and then apply these to helium as well as developing a more sophisticated analysis of hydrogen involving the fine and hyperfine structure. We now have the tools to analyse more complex atoms with many electrons – we learn about electron shells and the Periodic Table.

Next come diatomic molecules and then an overview of the quantum treatment of bulk solids. Now we begin to understand the real differences between insulators, semiconductors and full conductors. In the final chapter we look at the interaction between atoms and electromagnetic radiation, treating the former quantum mechanically and the latter classically. And that’s it.

Some summary thoughts. SM358 is a very thorough, somewhat conservative and rather practical first course. It deliberately doesn’t get involved in populist worries about ‘the meaning of quantum mechanics’: the focus is very much on learning concepts and techniques. This is wholly to be applauded.

The concepts are of course very alien and the course material really needs to be read at least twice. The first time to ‘load the concepts’ - hard work because of their novelty. The second time to knit them together into a holistic totality. Revision for the exam is very important for this final consolidation and sufficient time needs to be budgeted.

Overall, the course is somewhat similar to the material covered in “An Introduction to Quantum Physics” by A. P. French and E. F. Taylor. I found the extra depth in this textbook sometimes helpful in illuminating concepts.

What is barely hinted at is the elevated ladder of which this course is merely the first rung. The next step would be a graduate-level 'proper' Hilbert space development of non-relativistic quantum mechanics. This would be complemented by Quantum Field Theory, which as the name suggests quantizes the classical fields and unifies quantum mechanics with special relativity to give us the Standard Model. And then there is the search for grand unification, combining the four forces of nature into one coherent framework. This takes us to quantum theories of gravity, most notably String Theory.

To climb this ladder would probably take an ambitious young physicist most of their twenties.