Atomic Orbital Surface
Atomic Orbital Surface is a spectral surface, given by a parametrisation, immersed.
Open Atomic Orbital Surface in the interactive viewer →
aperiodic def-parametric immersed implemented spectral
Properties
- Family
- spectral
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: hydrogenic orbitals need Laguerre polynomials and spherical harmonics; outside the language. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- E. Schroedinger, "Quantisierung als Eigenwertproblem", Annalen der Physik 384 (1926) -- the wave equation whose bound states these are.
- The closed form psi_nlm = R_nl(r) Y_lm(theta, phi), with R_nl an associated Laguerre polynomial and Y_lm a spherical harmonic, is standard; see L. Pauling and E. B. Wilson, "Introduction to Quantum Mechanics" (1935), chapter V, for the derivation and the tabulated low-n forms.