Δu = 0 in 2D iff u = Re(f) for holomorphic f locally. Mean-value property, maximum principle, Poisson kernel on disk.
Harmonic function & potential
Related concepts
- Holomorphic function
- Harmonic function (Δu = 0): mean-value property and max principle
- u = x² - y² harmonic: Δu ≡ 0, mean over circle ≡ 0 = u(0)
- Dirichlet problem (Laplace equation)
- Mean-value property (harmonic functions)
- Dirichlet principle (1850)
- Jaynes–Cummings dressed states: H = ℏω(a†a + σ_z/2) + ℏg(aσ₊ + a†σ₋); harmonic Rabi oscillations