Quantum-elastic bump on a surface

Abstract

We use an exact solution of the elastic membrane shape equation, representing the curvature, which will serve as a quantum potential in the quantum mechanical two dimensional Schrodinger equation for a (quasi-) particle on the surface of the membrane. Surface curvature in the quasi one-dimensional case is related to an unexpected static formation: on one hand the elastic energy has a maximum where surface curvature has a maximum and on the other hand the concentration of the expectation value to find the (quasi-) particle is again where the elastic energy is concentrated, namely where surface curvature has a maximum. This represents a particular form of a conformon.

References in corpus (2)

• Effect of conformations on charge transport in a thin elastic tube
• Quanta of Local Conformational Change: Conformons in alpha-helical proteins

Cited by in corpus (4)

• On the variation of curvature functionals in space forms with application to a generalized Willmore energy
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• Electronic states in a quantum Beltrami surface
• Quantum particle on a surface: Catenary surface and Paraboloid of revolution