This semester I am the luckiest prof. on campus. In addition to all the obvious reasons, including the finally melting snow, I get to teach the perfect course. The stars align for this one: it is an elective course for senior undergraduate students, so the students tend to be bright and well-motivated. Unlike so many other courses, this one is coherent, with well-defined and feasible objective and a focused target audience. And, best of all, it is a course in quantum mechanics.

Back in the days when I was an undergraduate student, learning quantum mechanics changed the course of my studies. Up to that point I immersed myself in down to earth topics such as set theory, mathematical logic, model theory, and all this good stuff. Luckily, I discovered quantum mechanics before things got too abstract, which led me more or less directly to my current concrete and hands on occupation. Since then, quantum mechanics has been close to my heart, I am really happy to be able to teach it.

The course it titled “Applications of quantum mechanics”, and is covering the second half of the text by David Griffiths, whose textbooks I find to be uniformly excellent. A more accurate description of the material would be approximation methods for solving the Schrodinger equation. Not uncommonly in the physics curriculum, when the math becomes more demanding the physics tends to take a back seat, so we are going to spend quite a bit of the time on what is essentially a course in differential equations, using WKB approximations and perturbation theory and what not. To counter that, I am looking for short and sweet applications of quantum mechanics. Short topics which can be taught in an hour or less, and involve some cool concepts in addition to practicing the new mathematical techniques.

So, this is the first audience participation question of the year, what is your favorite application of quantum mechanics?

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on January 6, 2009 at 5:53 pmNilsWhere do you teach?

on January 6, 2009 at 6:23 pmDemianI am teaching the exactly the same course this semester using exactly the same book. I will be interested in hearing replies to this post.

on January 6, 2009 at 6:31 pmdberensteinMoshe:

I’m partial to single photon quantum cryptography (although I believe this is not exactly what you were talking about).

Another fun one is alpha tunneling from a nucleus to explain some aspects of radioactivity (strong nuclear decays). It is a toy model, not from first principles.

If you allow many-body stuff, there are a lot of other cool things I would add to the list.

on January 6, 2009 at 8:11 pmdominicI don’t know if it’s suitable for your course, but one of the simplest and more revealing exercises we were taken through in my undergraduate course was the calculation of the probability of one of us tunneling out of the lecture hall.

It was a very silly example, but it was a lot of fun to go through.

on January 6, 2009 at 8:30 pmJSDHi Moshe,

being an undergrad studying QM I was fascinated with the connection between symmetry and degeneracy, and I was also quite tired of electron in boxes. After studying perturbation theory everything changed: the idea of energy levels of the Hydrogen atom and how breaking the symmetry of the Hamiltonian by including external fields (E or B) could produce the splitting of degenerate levels was spectacular!

Other examples were the theory of bands in solids and the alpha tunneling mentioned by David.

Good luck

on January 6, 2009 at 8:43 pmChrisIt’s probably more than an hour, but an introduction to lasers and/or LEDs could be pretty useful. I have vague memories of an entire grad-level class (taken as a senior) on this and it was the first place where I saw QM used as a tool instead of the subject with seemingly artificial problems.

on January 6, 2009 at 9:03 pmSean CarrollYou must include quantum interrogation and the Zeno effect. Extremely cool, and the only drawback might be that they don’t require much heavy lifting in terms of solving the Schroedinger equation.

on January 6, 2009 at 9:23 pmsaintnekoI’m not sure if this is a quantum level effect or not, but if it is, going over the way shape-memory alloys function may be fun. (I know it has something to do with the atomic lattice structures of the alloys, I just don’t know enough to say whether or not that is quantum-applicable)

I know it’s not in vogue, but maybe a discussion on the observation that is apparently necessary for quantum mechanics to produce reality as we know it? Not in a “you need to think about this to solve it” kind of way but in a “you need to be aware of this because it’s an apparent consequence of reality and will at some point may need to be resolved.” Currently, for all practical purposes, things work very well. But the same was true of Newtonian physics. At some point, we’ll be at that stage again. (And if you don’t believe me, go read some history and see how many people have proclaimed that “all that ever need be known now is, and only a few details remain to be worked out.” Those claims just imply a lack of imagination.)

I intend to study quantum mechanics in the future as I want to eventually be involved with the nanotech industry, but I’m afraid at the current time I only have a semi-lay perspective (am currently studying electron microscopy) so please be gentle if I have appeared foolish in my comments.

on January 6, 2009 at 11:20 pmtg1. Aharanov-Bohm effect and its variants like quantum random walk in the absence or presence of a magnetic field (‘weak localization/delocalization’).

2. LASERS and MASERS.

3. Quantum tunneling and its applications such as Josephson effect, ‘symmetry restoration’ in finite systems.

4. Concept of identical particles and its consequences like existence of objects such as metals, (band) insulators, BECs.

on January 7, 2009 at 12:40 amErikI used the same book during my undergrad courses, but I was a second year student and this part was not optional. I also think griffiths books are really excellent to learn from (we also used it for electrodynamics and I bought it myself for particle physics).

This part of the book is really well suited to,

1. study vibrational levels of molecules and perhaps explain some results from optical spectroscopy. (my prof was an experimentalist in the field of molecular nano-

optics and spins)

2. Use the born approximation and explain why electrons in solids behave as nearly free (i.e. nuclei are SOOO much slower). The Born approximation is widely used in diagramatic expansions of perturbation series in condensed matter physics…

3. Bells paradox etc. as mentioned above. There are some really cool things to say about quantum crypthography using notions from conformal field theory, phase transitions and symmetry breaking but I think it will diverge to far from the original subjects of the book.

It is always great to think about the deeper meanings of QM, but I agree with Chris hat this part offers a practical approach to really calculate stuff.

I walked away from my course with that feeling as well.

on January 7, 2009 at 3:15 amLionelThis is rather pedestrian but I found the correspondence between pure state/mixed state and closed system/open system enlightening, e.g., how tracing over part of your density matrix gives you a mixed state which is in some cases even thermal (e.g., two harmonic oscillators after Bogoliubov transformation, which is a prototype for Unruh radiation). The connection with thermodynamics is also interesting.

Other topics include the supersymmetric quantum harmonic oscillator as a prototype for supersymmetry in general.

A big eye-opener for me was environmentally-induced superselection as a mechanism for decoherence, which finally settled my misgivings towards things like collapsing wavefunctions. I think too many people graduate believing that quantum mechanics is a complete theory save for some inconvenient Cartesian dualistic hang-ups. Do I get my 30 points at the door?

on January 7, 2009 at 3:55 amMosheLionel, I thought we stopped counting (at least I hope so, for my own sake).

Thanks everyone for all the suggestions, they are good ones. Keep them coming!

on January 7, 2009 at 8:35 amNathanHaving just taken a second semester course on quantum mechanics out of the second hald of griffiths from a particularly good professor, I’d say I’m uniquely qualified to answer this.

I think my two favorite lectures were on the quantum zeno paradox (although we just touched on this… it’s still so incredibly weird), and, while strictly not in griffiths, the final lecture we had, on the Dirac equation, was really cool.

on January 7, 2009 at 11:07 amMatt LeiferI’d second topics from quantum information. Cryptography and teleportation can easily be taught in a small amount of time.

The book by Aharonov and Rohrlich is a good source of unusual quantum effects which can be used to build intuition. There’s lots of material on geometric phases and the modular variables stuff is fun, although I don’t know how useful any of this is.

For foundational stuff, e.g. Bell’s inequalities and the Kochen-Specker theorem, I’d take a look at Peres’ book. Perhaps surprisingly, as well as the foundational significance, there are simple quantum information applications of this stuff, but it’s a bit too new to have made it into any textbooks yet.

on January 7, 2009 at 6:00 pmMosheBack in the days I took a course from Aharonov, called “famous paradoxes in physics”. It consisted of him giving us a paradox to solve, then shooting down all our attempts to solve it. Great fun, mostly for him… I did not realize this became a book, I think I’ll go to a book store now. Thanks Matt.

on January 8, 2009 at 2:05 amcarlbrannenI think that what Julian Schwinger did with the Stern-Gerlach experiment and his measurement algebra is the most elegant part of QM. I created a website devoted to the subject with links to the original papers at

http://www.MeasurementAlgebra.com

This is sort of like density matrices but is slightly different in that one does not require a quantum state to have trace = 1. For spin-1/2, all operators and quantum states are represented by 2×2 matrices. Instead of the usual density matrices, it’s beam oriented. As operators, “0” means a beam stop. “1” means no modification to the beam, at least as operators. And the projection operators mean devices that only allow a particular spin direction through.

As states, “0” means no particles, “1” means a beam with full amplitude and no complex phase. This is enough to do Berry-Pancharatnam phase calculations very easily.

on January 8, 2009 at 4:19 ammcguiganI think the two and three state systems are simple but

have interesting advanced applications as discussed in the Feynman lectures. These can include neutral Kaon

mixing and decay, neutrino oscillation and the seesaw mechanism in particle physics. These need quantum field theory to do full justice, but still a lot can be done with basic quantum mechanics.

on January 10, 2009 at 3:16 pmHaelfixNeutrino oscillation is a really good one.

I also like throwing in some Feynmann lectures material on molecules to get some simplified interacting models.

on January 12, 2009 at 1:57 amcarlbrannenI also vote for neutrino oscillation; it is particularly confusing the way it is usually taught. It makes perfect sense as an interference calculation between the mass eigenstates (rather than oscillation of the flavor eigenstates).

on January 15, 2009 at 4:54 pmJerryInfinite spherical potential well and applications to energy levels in Nuclear Physics. See Prussin’s Nuclear Physics for Applications.