Surfaces of revolution via the Schrödinger equation: Construction, integrable dynamics and visualization

摘要

Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schrödinger equation (infinite well, harmonic oscillator, Coulomb potential, Bargmann potential, etc.) are analyzed and visualized. The properties of such surfaces are discussed. Two types of deformations (evolutions) of the surfaces of revolution, namely (1) preserving the Gaussian curvature and (2) via the dynamics of the Korteweg-de Vries (KdV) equation are discussed.