SkunkyArt | lonkirou — Bessel Tutorial II

This doesn’t only work with cylinders. You can try it with all kinds of shapes. You’ll just get other hero and sidekick functions. For boxes you get sines, for spheres you get a sidekick that’s super famous with chemists called spherical harmonics .

The cup and drum equations are only valid if the ripples are small.

If you can’t make the Bessel function appear in your cup, try a bucket. Gently knock at it with the right frequency and there you go.

The pattern in your eyes is called Airy disk. It also shows up in microscopes or all kinds of optics with circular apertures. The brightness isn’t exactly (J_1(r)/r)² though, because you can’t really measure seen brightness. But if you get some sensor and measure the light intensity, you get something like (J_1(r)/r)²

In the skin effect bit, actually j(r) = Re J_0(br). Re means real part of the complex number “J_0(br)”

The quantum mechanics equation was the stationary Schrödinger equation in position representation for a free particle.