Surfaces of Revolution via the Schroedinger Equation : Construction, Integrable Dynamics and Visualization

Details Surfaces of Revolution via the Schroedinger Equation : Construction, Integrable Dynamics and Visualization Surfaces of Revolution via the Schroedinger Equation : Construction, Integrable Dynamics and Visualization

1997-10-30

arxiv.org/abs/solv-int/9710027v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 27 figures

Scientific paper

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 Schoedinger 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), namely 1) preserving the Gaussian curvature and 2) via the dynamics of the Korteweg-de-Vries equation are discussed.

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