New Operator: AngularMomentum

[MikaelSlevinsky]

This one is just about as fundamental as the Laplacian. For complex spherical harmonics and Zernike polynomials, it's diagonal. Other multivariate OPs may have nontrivial representations. In polar coordinates, it's ∂/∂θ; in spherical coordinates, it's ∂/∂φ. Or in both systems, it's x ∂/∂y - y ∂/∂x. Since it's spectrum "separates orders," it is complementary to the Laplacian which "separates degrees."

[dlfivefifty]

What would you call r ∂/∂r = x ∂/∂x + y ∂/∂y?

[MikaelSlevinsky]

I don't know, a Cauchy-Euler operator? https://en.m.wikipedia.org/wiki/Cauchy–Euler_operator

A Homogeneous operator? https://mathworld.wolfram.com/EulersHomogeneousFunctionTheorem.html