Motion in an Asymmetric Double Well

Abstract

The problem of the motion of a particle in an asymmetric double well is solved explicitly in terms of the Weierstrass and Jacobi elliptic functions. While the solution of the orbital motion is expressed simply in terms of the Weierstrass elliptic function, the period of oscillation is more directly expressed in terms of periods of the Jacobi elliptic functions.

12 pages, 10 figures; references added

References in corpus (4)

• The double well potential in quantum mechanics: a simple, numerically exact formulation
• Bose-Einstein Condensates on slightly asymmetric double-well potentials
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials
• Notes on the Weierstrass Elliptic Function

Cited by in corpus (5)

• Exploring Isomerization Dynamics on a Potential Energy Surface with an Index-2 Saddle using Lagrangian Descriptors
• M2-brane Dynamics in the Classical Limit of the BMN Matrix Model
• Action-angle coordinates for motion in a straight magnetic field with constant gradient
• Turbulent aspects of BMN membrane dynamics
• Out-of-Time-Order-Correlation in perturbed quantum wells