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

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 Schrodinger equation (infinite well, harmonic oscilla tor, Coulomb potential, Bargmann potential, etc.) are analyzed and visualiz ed. The properties of such surfaces are discussed. Two types of deformation s (evolutions) of the surfaces of revolution, namely (1) preserving the Gau ssian curvature and (2) via the dynamics of the Korteweg-de Vries (KdV) equ ation are discussed. (C) 1999 Elsevier Science Inc. All rights reserved.