Schrödinger problems for surfaces of revolution-the finite cylinder as a test example

✍ Scribed by Gravesen J., Willatzen M.

• Book ID: 127404128
• Year: 2005
• Tongue: English
• Weight: 79 KB
• Category: Library
• DOI: 10.1063/1.1829376]

✦ Synopsis

A set of ordinary differential equations is derived employing the method of differentiableforms so as to describe the quantum mechanics of a particle constrained tomove on a general two-dimensional surface of revolution. Eigenvalues and eigenstatesare calculated quasianalytically in the case of a finite cylinder (finite alongthe axis) and compared with the eigenvalues and eigenstates of a full threedimensionalSchrödinger problem corresponding to a hollow cylinder in the limitwhere the inner and outer radii approach each other. Good agreement between thetwo models is obtained for a relative difference less than 20% in inner and outerradii"