Wednesday, April 9, 2014

Discovery of a Tetraquark

Interesting discovery coming out of CERN here (CERN's press release here).

The scientists claim they discovered a four-quark particle, or tetraquark, composed of a charm, anti-charm, down, and an anti-up quark. The particle would appear to be roughly (or possibly even exactly) a bound state of two mesons, that is two pairs of color-anticolor quarks; for example red-antired and blue-antiblue. The charges of the charm and anti-charm obviously cancel, leaving -13 from the down and -23 from the anti-up, for a total charge of -1.

I can't speak to the quality of this research per se, but I do remember the excitement and subsequent let down over the pentaquark, so I'm going to wait to hear what the wider particle physics community concludes about this latest finding. Still, it's a pretty cool finding.

Tuesday, April 1, 2014

Is Spin a Relativistic Effect? Levy-Leblond and First Order Wave Equations

One of the earliest concepts we cover in atomic structure is the concept of electron spin. We are taught to think of the electron's spin the same way we think of its charge; there's no particular reason a particle should have spin according to quantum mechanics, it merely happens to. Once the electron has spin, we include it (when necessary) as an additional parameter in the wave-function. Some texts state that spin is a relativistic effect that must be included as an ad hoc addition to nonrelativistic quantum mechanics, for example in Quantum Chemistry by I. Levine chapter 10 we find the claim:
In the nonrelativistic quantum mechanics to which we are confining ourselves, electron spin must be introduced as an additional hypothesis.

Other undergraduate and graduate texts on quantum mechanics I have examined appear to take more or less the same view. But is it really true? Is it really impossible to justify spin without invoking relativity? In this post I plan to demonstrate that it is not. But first, a little background.

Background: The Discovery of Spin

In retrospect, spin was first discovered in 1922 by Otto Stern and Walther Gerlach, though they didn't realize it at the time. In the now famous Stern-Gerlach experiment, they found that an electron passing through a magnetic field will be deflected in one of two possible directions. (Historically, they found this to be true for gaseous silver atoms, but the reason was later established to be because of the spin of the single unpaired electron.)