Acquiring a physics degree is no easy feat, and one of the great challenges is Quantum Mechanics.  The aspiring physicist is introduced to the subject as a sophomore in a class called "Modern Physics".  (Unlike modern art, modern physics began in 1900.)  I like modern physics as a subject, but disliked modern physics as a class because Professor Lomanitz was the sort of sinister fellow who summoned his pupils at the unnatural hour of 8am.  In my undergraduate years, my brain was ill-prepared before 9:30am to operate even my alarm clock and shower.  Einstein's theory of relativity was completely beyond comprehension until after noon.  I learned the material considerably better in the evenings studying in solitude than I did from the crack-of-dawn tutelage of Dr. Lomanitz.  I succeeded in Modern Physics principally through self-study and considerable homework collaboration with my friend Jethro.

The next year Quantum Mechanics came on full bore, with a three credit-hour course dedicated exclusively to the subject, Physics 380--"Introduction to Quantum Theory."  Anyone who has pursued a difficult degree understands how ominous it is to see the word "introduction" featured in the name of a course with a long list of cascading pre-requisites.  This was Fall 1990, and I was starting my fourth year of college.

The most frustrating thing about Quantum Mechanics was the textbook, created by some feeble-minded clods at M.I.T.  Once I had to retrieve the text from the 7th hole of the New Mexico Tech golf course after spending two hours trying to solve an electron tunneling problem, only to realize there was a critical but subtle typographical error in one of its formulas.  Armed with that loathed book, I would have surely won any distance textbook hurling competition.  Here is a sample of the sort of material we attempted to learn from it:

Thus, to take an extreme example, if we consider an electron in the n = 1 orbit of a uranium atom, with Z = 92 and Q 91e (since the inner orbit is shared with another electron) the value of v/c is about 2/3, according to Eq. 12-24.  In this case, relativistic effects are clearly very important; indeed one can recognize that a thoroughgoing relativistic analysis from the beginning is obligatory, rather than an analysis based on the nonrelativistic Schrödinger treatment with minor relativistic corrections added later. One can guess that in such circumstances the splitting of levels of the same n but different j will be relatively much greater than in hydrogen, more or less in proportion to Z2. The energy levels according to the exact form of Dirac's relativistic theory (ignoring the nuclear mass correction) are in fact given by the following formula: (12-25)

It doesn't take more than one typographical error in such an equation to explain why so many physicists are bald.

The second most frustrating thing was the professor--Dr. Bill Winn--whose sedate instructional style made the class one of the most tedious I'd encountered.  Even at the tolerable hour of 10am, it seemed like it would never end.  It would be a year before I would learn that under different circumstances he could provide far greater inspiration.  But it was in Quantum Mechanics that I encountered one of the great dark evils of advanced physics and mathematics--the condensed theoretical equation.

Any physicist who presents an equation such as

E=mc²

cannot reasonably do so without the immediate explanation "Matter is a form of energy, and the quantity of energy produced from that conversion is equal to the mass times the square of the speed of light."  It may not be abundantly clear to the layman, but the formula sums up a fundamental and amazing concept in a most tidy form that is easy to explain in a single sentence. Unfortunately, many topics in Quantum Mechanics cannot be so easily summarized. Big hairy concepts are condensed into equations, with much more cumbersome concepts than "energy", "mass" and "the speed of light."  They have only the most tenuous connection to concepts that can be described in fewer than 500 words.  If you are sitting in quantum mechanics class and look up at the board at some random moment, you're likely to see something completely unlike E=mc², and much more like specimen (12-25) above.

As a result, instead of calling ²Z^{2, "}the square of the fine-structure constant times the square of the atomic number of the nucleus", the well-meaning physicist starts calling it simply "alpha-squared, Z-squared" if only to hasten the conclusion and preserve his voice.  The menacing result of this terminology consolidation is that the student is presented with equation after equation on the blackboard, and page after page in the textbook, filled with concepts that have been transformed into glyphs without any handy index to look up what they mean.  I found my brain's glyph glossary completely overwhelmed by quantum mechanics, and I sometimes found myself rifling through the book searching for the definition of a simple glyph such as .  While I was doing that, Dr. Winn had already filled another board panel with so many equations featuring a that they had cancelled each other out.

I specifically remember failing to remember the meaning of certain glyphs contained in equations such as

The Schrödinger wave value is represented by an upper case Greek letter Psi----which some of us referred to as "pitchfork."  I have a vivid memory being mesmerized by the sheer abundance of glyphs on the blackboard and struggling to remember the meaning of the mathematical term "pitchfork star pitchfork".  All the while, Dr. Winn scrawled pitchfork after pitchfork on the board.

Unexposed to the potential interest Dr. Winn was capable of generating, Jethro and I coined the phrase "Lose with Winn."  Jethro wanted to graduate and get out of Socorro, even with a barely-satisfactory grade.  Because I was having so much fun with extracurricular activities like running the school newspaper Paydirt, I used my difficulty in Dr. Winn's class as the precipitating trigger to stay a fifth year at Tech, dropped the class on the last permitted day.  I hoped that another professor would teach Quantum Mechanics the next year.

Operation Highway Robbery I

In his final act of defiance, Jethro concocted an idea to convey our sentiment of the difficulty of Quantum Mechanics class: we would obtain a DO NOT PASS highway sign and place it in the classroom for the final exam.

Late the night before the exam, Jethro and I set off into the desert in my trusty Mazda pickup truck.  We found a nearly-abandoned section of a remote road, identified a sign in an especially remote area and set about retrieving it.

On many roads in the desert, you can see for 10 or more miles, putting them among the rare environments where you don't need a dedicated lookout to conduct a covert operation.  Nothing sneaks up on you in places like that.  But the whole point of DO NOT PASS signs is that they're located near landforms obscuring the road ahead.  Jethro volunteered to extricate the sign from its post if I served as lookout.  I picked a spot about fifty feet down the road from which I could see around the bend and alert him in the unlikely event that any vehicles approached.

The odd thing about highway signs is how darn big they are. When you see a sign as you drive past at 70 mph, they don't appear so big. Sometime when you're driving, though, compare the size of a speed limit sign to another vehicle and you'll see how large they are. Our target was a 3x5-foot reflectorized plywood sign, bolted at the top and bottom to a steel post.

Jethro's approach to solving any problem is to get the hard part out of the way before finishing with the easy part.  The upper bolt--about nine feet off the ground--was the hard part.  So he climbed a few feet up the adjacent embankment, leaned over, and attacked the bolt with a wrench.  The bolt didn't budge.  He sprayed some Liquid Wrench on the bolt, waited a moment, and took the wrench to it again, heaving with all his considerable might and weight.  The bolt creaked and gave way; within a few minutes, he had the entire upper bolt removed.  No cars had come by, but I remained on lookout duty.

Then Jethro set to remove the lower bolt, about four feet off the ground.  He leaned over to inspect it.  About that time, in true Wile E. Coyote fashion, the sign realized that it was held in place by exactly one bolt and that its center of gravity was well above that bolt.  In Classical Mechanics class, we called that Unstable Equilibrium. The mass sought a lower energy state, and swung around.  The only obstacle to the large plywood sign as it swung was an occipital horn--the back of Jethro's skull.

Standing fifty feet away, I happened to be looking at Jethro as the sign careened down; my shouts reached him too late.  Konk!  Jethro looked like he had been unplugged--he went limp and fell to the ground like a sack of potatoes.  Fortunately, he had been leaning over, so he fell only a few feet onto the hard ground.  I ran toward him, and he regained consciousness as the sign pivoted creakily back and forth on the remaining bolt.  "Did that just hit me?" he asked.  "It sure did, son.  Are you OK?" I replied.

Jethro felt a bit odd, but generally all right, and asked me to verify his brain's effectiveness.  I asked him a question regarding an electron in a one-dimensional potential well--a topic we had reviewed the previous night.  He had no trouble calculating the answer.  His brain seemed up to its normal operating ability.  Nonetheless, Jethro avoided sudden motion while we removed the final bolt, freed the sign from its post, deposited it into my pickup truck, and fled back to campus.

A full-size road sign is an extremely conspicuous object to carry about campus, and we wanted to plant our plunder without being caught.  Jethro and I arrived in Dr. Winn's class about an hour before the 9am final.  After placing the sign, Jethro remained to cram as many last-minute facts as he could into his recently-shaken brain.  Having dropped the class, I cheerfully went home to bed.

Jethro reported that Dr. Winn arrived in class, looked at the "DO NOT PASS" sign on the blackboard, smirked and said "Does that apply to this exam?" Jethro completed the exam--we'll never know if his concussion hindered or helped his performance--and he graduated with a barely-passing grade of C.  He fled from Socorro to Nashville to continue life as a degreed Bachelor.

Operation Highway Robbery II

The next year, when the schedule was published for the Fall 1991 semester, I saw that Dr. Winn was again the professor for Quantum Mechanics.  The devil you know, I optimistically surmised, can be better than the professor you don't.  Several other Beta operatives were in that class.  Operative Fingers, Operative Ratchet, and Operative Goldilox joined me (Operative Sasquatch) in forming the largest contingent of Stealth Force Beta members ever enrolled in any class.  We were prepared for the worst.

The second time around, however, things got off to a different start.  Dr. Winn's wife had purchased an abundance of Girl Scout cookies, so one fine Monday morning, Dr. Winn presented the surplus to us.  All the students were very happy that day, for we had never been given cookies by a physics professor before.  (Such things weren't unheard of in other departments--for instance, Human Sexuality had been taught sometimes in the town donut shop.  But that was the Psychology department--Physics had a different standard.)  After the cookies, the level of joviality in Dr. Winn's Quantum Mechanics class took a dramatic and permanent turn upward.

Students started bringing their own supplies of tasty morning foodstuffs, and the class became much less formal.  Dr. Winn enthusiastically supported the additional interest in class.  When assigned an electron tunneling problem, Fingers wrote his solution in the form of a poem titled I Am an Electron, explaining from its own anthropomorphized perspective how the electron leapt from one energy state to another.   Jason Aufdenberg used a sharp knife to slaughter a rubber chicken when he described  the "voodoo mathematics" involved in calculating Heisenberg's Uncertainty Principle.  And one day, when Dr. Winn turned his head to write something on the board, I gave a signal and every last student in class rapidly donned a pair of "spacey eyeglasses" with built-in cardboard eyes that we had purchased from the Oriental Trading Company for $6.  Dr. Winn looked back, resumed writing another Greek letter or two on the board, then turned around with a very odd expression on his face and burst out laughing.  Quantum Mechanics my first time had consisted of dispassionate lecturing being weakly absorbed by largely disinterested students, Quantum Mechanics my second time--with precisely the same professor and a similar group of students--was an engaging, fun experience.  Against this backdrop, it was considerably easier to ask an occasional stupid question--"What's pitchfork star pitchfork mean, again?" Professors take note: this is the sort of dramatic improvement in professor-student interaction spawned by two boxes of Girl Scout Cookies!

Nonetheless as the final exam approached, the rigorous nature of the class warranted a repeat of Operation Highway Robbery.  This time, we decided to expand the mission--we would get not just a "DO NOT PASS" sign, but also a "NO PASSING ZONE" sign.  This time, we sought to avoid any concussions, so instead of one lookout and one sign remover, we had two lookouts and two sign removers.  Late the night before the exam, Ratchet, Fingers, Goldilox, and I drove down the same road to find our targets. Goldilox was far around the curve,  Fingers was close enough to see both her and the sign extraction operation.  Ratchet and I dismantled the bolts holding the signs to their posts.  (We started with the bottom bolt.)  This year's "DO NOT PASS" sign was a fair bit smaller than its predecessor, which made it easier to carry.  We had no difficulty depositing both signs into my pickup truck. We hauled them back to school and placed them at the site of the next morning's final exam.  We all arrived before Dr. Winn for class--this time when he walked in, he gave a hearty laugh and said "Not this again!"  It was worth dropping Quantum Mechanics the first time just to experience how much more fun it could be the second time.

The scene of Operation Highway Robbery II before Dr. Winn's Quantum Mechanics exam. (Sign text restored from flash washout.)