Ah, yes indeed, that answers it. I wasn’t sure if the term was referring to something specifically in QM, for a particular medium, etc. (There are plenty of equations in QM that *look* simple and innocuous, after all.)

I’d also note that this is the first time I’d seen “capital letters, as a rule, are operators” called out explicitly. Everything else I’ve seen seemed to assume you’d pick it up eventually – which I guess is true, but it’s quite nice to see the context made explicit.

]]>Whoops — typo. Fixed.

A free wave is a solution to the wave equation in the absence of any background forces or potentials; it’s the equation which describes a wave propagating in a medium without any forces on it. It’s the same equation for, e.g., sound waves, light waves, and so on, and its solution (in an infinite, empty space, so that there aren’t any complicated boundary conditions) is . That’s a sine wave with wave number k, with the wave peaks moving along at a velocity .

All of the usual rules of optics and so on follow from this; e.g., you can get the formula for the interference pattern you see when you push light through slits, gratings, and so on by adding up a bunch of free waves of the relevant sort. (For light, the wave velocity is just the speed of light)

Does that answer your question?

]]>Some more background of what a “free wave” is would have been nice.

]]>It will turn out that pretty much everything in nonrelativistic quantum mechanics comes down to understanding this one equation and the things one can measure it.

Undergrad level QM became much easier for me when I realized the entire course (well, all the problems given anyway) was about boundary conditions. Unfortunately, this realization came after I took it.

Also, there’s an interesting discussion going on at Chad Orzel’s blog about teaching Stat. Mech. that matches well with my experience.

]]>It’s a virtuous cycle; writing them makes me feel like I’m doing something productive while I avoid actual work.

]]>(It has the added benefit that reading your posts makes me feel like I’m at least doing something productive while I avoid actual work.)

If only my insane ideas happened to match those of de Broglie… sigh.

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