Exact zero-energy solution for a new family of Anharmonic Potentials

Abstract

An explicit, oscillatory solution of the type r = [A + B sin(wt)]exp(a) is found for the zero-energy one-dimensional motion of a particle under a specific family of anharmonic potentials. We present a new parametric family of anharmonic potentials for which one is able to obtain closed analytical solutions for the trajectories of zero-energy.