A quantum of science

In physics we do things and afterwards worry about whether they worked

Category Archives: Quantum

Hilbert spaces from the mathematician’s perspective

Yesterday I came across these notes by Terence Tao on his blog for one of his Analysis courses at UCLA. They treat Hilbert spaces as part of mathematical analysis: a new perspective for those of us who first came across the topic while learning quantum mechanics. They’re embedded with exercises, and quite readable. Also, this is Tao, so they’re definitiely worth having a look at:

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Quantum metrology

According to Wikipedia, quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, in particular exploiting quantum entanglement.

If you are interested, you might want to take a look at this. It is a paper entitled Ensemble based quantum metrology.  Quoting the abstract:

We consider measurement of magnetic field strength using an ensemble of spins, and we identify a third essential resource: the initial system polarisation, i.e. the low entropy of the original state. We find that performance depends crucially on the form of decoherence present; for a plausible dephasing model, we describe a quantum strategy which can indeed beat the standard quantum limit.

Feynman and Hibbs

Feynman’s path integral formulation is important in quantum physics. Some people learn it when they come to do Quantum field theory where it plays a central role. However, there is a book that introduces a sophisticated physics student with reasonable background to path integral in non-relativistic quantum mechanics, “Quantum mechanics and path integrals”, by Feynman and Hibbs.

It is highly recommended. It is a book full of deep and extraordinary insights, as one expects from Feynman. It is not a standalone textbook in QM – it should be used in conjunction with a conventional text.

What I love the most about this book is how quickly the laws of physics are laid out – by the end of chapter 2 they are in place, and the rest of the book is applications. It is an approach similar to the one he adopts in Vol. 2 of Feynman Lectures on Physics where Maxwell’s equations are laid before you in their finished form in the first chapter and the rest of the book is devoted to understanding those equations.

The original edition, 1967, was riddled with errors. The new one is amended and available on Amazon at the end of September this year, and being a Dover costs an agreeable £15. Should you happen to come across the first edition, Daniel Styer’s errata is an absolute must. It is available here.