Sean Carroll at Preposterous Universe:
The basic issue is that people hear the phrase “quantum mechanics,” or even take a course in it, and come away with the impression that reality is somehow pixelized — made up of smallest possible units — rather than being ultimately smooth and continuous. That’s not right! Quantum theory, as far as it is currently understood, is all about smoothness. The lumpiness of “quanta” is just apparent, although it’s a very important appearance.
What’s actually happening is a combination of (1) fundamentally smooth functions, (2) differential equations, (3) boundary conditions, and (4) what we care about.
This might sound confusing, so let’s fix ideas by looking at a ubiquitous example: the simple harmonic oscillator.
More here.