Fast forward to last night: Just as we were starting to clean up from dinner, the phone rang. Kim answered, and then said, "So you're having trouble with quantum mechanics? Sure, I'll get him." She handed the phone to me, and in response to my inquiring look she explained, "It's A---."
It turns out that A--- has the dubious fortune of taking classes from both Kim and me this semester, so when her study group got stuck on stuff for my class, she knew how to reach me. After a couple minutes of attempting to help over the phone, one of the folks in their group said, "We've got lots of questions on this stuff: can we just come talk to you in person?"
I paused for a moment as several thoughts flashed through my head: "Are you kidding? We've got to clean up and start moving toward bedtime." "This would be delightfully random." "Studies show high retention rates for students who make strong connections with faculty in their first semester of college." So I responded, "Sure! Here's our address." And a few minutes later, three students showed up at our door.
They stuck around for half and hour or so, maybe a bit more, and it went really well: with some extra hints and nudging from me, I think all three of them really solidified their understanding of the topic. They also looked like they were having fun, and none of them could quite believe that it was real. (After ten or fifteen minutes, one of them randomly exclaimed, "Hey, remember that time in freshman year when we went to a professor's house at night for help on our homework?") It was fun, and I like to think that it had a positive impact, too.
Namely, how to calculate probabilities when measuring the spin of an electron in a specified superposition state. Maybe I should have looked for some visually simpler way to represent superposition states than Dirac's ket notation, but I don't really know of a better alternative.