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Carl Mungan, United States Naval Academy
Solving for the eigenstates and energies of a hydrogen atom is a standard problem in introductory quantum mechanics. The radial part of the wavefunction exponentially tails away to infinity. But what happens if the atoms are confined, as might be an approximation of an exciton in a quantum dot? Then we must impose the boundary condition that the radial part goes to zero at some finite radius rather than at infinity. That in turn means we need to keep the second solution of the Schrödinger equation, known as Kummer functions. Read more about this analysis on page 860 of the November 2013 issue of the American Journal of Physics. Variations on this problem are a one-dimensional simple harmonic oscillator confined between two plates off which it bounces elastically, or a point charge in a capacitor (as a model of a biased quantum well).
There is an interesting study published in Physical Review Special Topics–Physics Education Research in the January 2014 issue about a comparison of different methods to compute a particular partial derivative involving a van der Waals gas. I present my own short solution to the studied problem at http://usna.edu/Users/physics/mungan/_files/documents/Scholarship/PartialDerivativeVanDerWaals.pdf.
Page 434 of the October 2013 issue of The Physics Teacher has an article entitled “Variations on the zilch cycle.” A zilch cycle has a “figure 8” shape on either a P-V or T-S graph, chosen so that the two lobes of the “8” have equal area but are traversed in opposite directions. That way, both net work and net heat are zero during a cycle. A zilch cycle is thus intermediate between a heat engine (which converts net heat input into work output) and a refrigerator (which converts work input into a net heat transfer). Readers should be alert to catch and correct a number of typos in the equations in this article, however.
Some interesting experiments using a Levitron (magnetically levitated spinning top) are reported on page 67 of the January 2014 issue of Physics Education, accessible at the IOPscience Journals page. By setting up outrigger magnets on and off the baseplate, one can tilt the spin axis of the top from the vertical all the way to a horizontal orientation! Analogs and applications of the precession and nutation are discussed.
A common science fair project is to make a battery. But typical projects use lemons which have very limited current density. A much better battery can be constructed using plates of aluminum and copper, table salt, and Drano drain cleaner, as described on page 1341 of the October 2013 issue of the Journal of Chemical Education. In a similar vein of science fair projects, see the article on page 1353 which considers the best way to construct a “soap boat” that is driven by differences in surface tension between water and another liquid (using alcohol rather than soap), as well as the article on page 1358 which cleverly considers how to build a reasonable solar cell out of household ingredients (well… except for the ITO glass slides used as substrates).
Is it possible to create molecules out of photons? Apparently yes, in a cold atomic gas, as discussed in the blurb from the article, Physicists create ‘molecules’ of light, in Physics World that references an article in Nature.
Disclaimer – The articles and opinion pieces found in this issue of the APS Forum on Education Newsletter are not peer refereed and represent solely the views of the authors and not necessarily the views of the APS.