Skip to main content

Interesting Topics from the APS TX Section Meeting and Other Places

More interesting ideas have come up in the last few days than I have time to pursue.  I'm capturing them here with a brief synopsis of each and a few pointers to documents so you can read more about it and I'll remember where to find it later.

We attended the +American Physical Society TX Section meeting last weekend in at Tarleton State Univesrity in Stephenville, TX.  I say we because it was my wife, the PhD physicist in the family, my brother-in-law, a physics grad. student and me.  I great time was had by all.

I got to see a second presentation of the  new approach to the Schrodinger equation presentation given by Dr.Schlich at Texas A&M last week.  This version was given by Dr. Scully of A&M[1][2].  During the talk, Dr. Scully   mentioned two things that caught my ear as I was preparing the slides from my talk, (apologies Dr. Scully.)  They were, the Bohmian potential and a paper where he mentioned they had solved the hydrogen molecule energy levels very accurately using high school algebra.

Bohmian Potential
This is the first I've heard of this.  Apparently it all started when de Broglie came up with the concept of pilot waves.  The idea as posited by de Broglie was that the electron was still a particle but that it was guided in its trajectory by the probability waves, (pilot waves) of quantum mechanics.  Interestingly, when I started looking into it, in addition to the off-handed remarks about it from both Schlich and Scully, I found a recent article about the idea in the American Journal of Physics and arXiv[3].  The article shows how the concept can be developed using the idea of wave packets following pilot waves, (picture 1 [3]).

These ideas can lead to the idea of the Bohmian potential which I haven't had time to really look up yet, other than to know that when you say Bohmian potential, people tend to say 'nonlocal'.

Hydrogen Molecule Solution Using Algebra[4]
It turns out the first author on this paper is another researcher in the departmetn here at A&M, so I hope to know way more about it soon!  For now, while I'd hoped to be able to use it on this weeks QM homework, I didn't quite get there.  This is a bit scattered, but Anatoly, (the author of the paper), recently gave a talk at the Texas Academy of Sciences meeting where he mentioned solving copuled harmonic oscillators in respect to a laser problem.  I think he used ideas that are ilucidated in this article form the AJP[5].

Cool Connections: Quaternions, The Dirac Equation, Helicity, Weyl, Neutrinos and More
The build-up:
1  During Schlich's talk on [1], he mentioned something to the effect of "and yes, here's where Weyl predicted neutrinos."

2.  David Hestenes came up indirectly at the TX SEction meeting.  He helped to author the force concept inventory[6], one of the mainstays of physics education research.  Hiis perhaps less-known accomplishment is his work on geometric algebra and spacetime algebra which each of which can show how it's easy to get to most of physics starting from quaternions.

3.  We're studying Dirac's equation in quantum mechanics this week.  The Dirac and Pauli matrices are both related to quaternions. Helicity came up in relation to Dirac's equation.

The delivery:
William Straub wrote an excellent article[7] detailing both how quaternions lead to the Pauli and Dirac matrices and how Weyl predicted the neutrino using Dirac's equation a decade or so ahead of everyone else in 1929.

Accidental Degeneracy and Special Relativity
After my post yesterday about accidental degeneracies in the hydrogen atom, +John Baez pointed me to a document]9] he'd written that has a plethora of additional information including how the whole thing is related to the group of Lorentz rotations.


1.  Scully and Schlich at PNAS
Schleich W.P., Greenberger D.M., Kobe D.H. & Scully M.O. (2013). Schrodinger equation revisited, Proceedings of the National Academy of Sciences, 110 (14) 5374-5379. DOI:

2.  Reference to Scully's TX Section talk

3.  Pilot Wave article from AJP and Arxiv

Norsen T. (2013). The pilot-wave perspective on quantum scattering and tunneling, American Journal of Physics, 81 (4) 258. DOI:

4.  Svidzinsky et al. on the hydrogen molecule

Svidzinsky A., Scully M. & Herschbach D. (2005). Simple and Surprisingly Accurate Approach to the Chemical Bond Obtained from Dimensional Scaling, Physical Review Letters, 95 (8) DOI:

5.  Article on coupled harmonics oscillators
Bhattacharya M., Shi H. & Preble S. (2013). Coupled second-quantized oscillators, American Journal of Physics, 81 (4) 267. DOI:

6.  Hestenes on the force concept inventory

7.  Hestenes on spacetime algebra

8.  Straub on quaternions and Weyl

9.  +John Baez on accidental degeneracies


Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…