Motion in an Asymmetric Double Well

TL;DR

This paper provides explicit solutions for the motion of a particle in an asymmetric double well potential using elliptic functions, offering clear formulas for orbital motion and oscillation periods.

Contribution

It introduces explicit solutions in terms of Weierstrass and Jacobi elliptic functions for asymmetric double well problems, enhancing analytical understanding.

Findings

Explicit solutions for particle motion are derived.

Oscillation periods are expressed via Jacobi elliptic functions.

The solutions facilitate precise analysis of asymmetric double well dynamics.

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.