Solução analítica do potencial de Morse em mecânica clássica

Abstract

Usualmente o potencial de Morseé estudado em contextos de mecânica quântica. Por outro lado, eleé relativamente pouco aplicado em problemas clássicos. Neste trabalho uma solução completaé encontrada para as equações de movimento clássicas para uma partícula submetida a esse potencial. Exemplos numéricos são apresentados para alguns valores fixos dos parâmetros. Palavras-chave: mecânica clássica, potencial de Morse, equação de movimento.Usually the Morse potential is studied in the quantum mechanics context. On the other hand, there are relatively few applications for classical problems. In this work, a complete solution for the classical equation of motion is found for a particle subject to this potential. Numerical examples are presented for a fixed set of parameters.

Solutions of the Fokker–Planck equation for a Morse isospectral potential

“…The form of the superpotential can be directly verified when we substitute the expression (14) in the Riccati equation (10), using V(x) instead of the Morse potential (12).…”

“…Several works have been dedicated to the study of the Morse potential from the quantum point of view [7][8][9]. On the other hand, few works about this potential from the classical point of view are relevant [10,11].…”

Morse lens [Invited]

“…which is an ideal and typical anharmonic potential with exact solutions for diatomic molecules in quantum mechanics, where D is the potential well depth, a is the potential well width, and x 0 is the equilibrium position (which we will set as 0 in this Letter). In addition, even in classical mechanics, this potential has analytical solutions [16] . By choosing E ¼ 0, the conformal lens in Eq.…”

“…Moreover, it will also become useful to design devices to transfer information accurately, for example, the Mikaelian lens with the Talbot effect. Therefore, to find more exact classical mechanics solutions similar to simple harmonic oscillators is vital [16] . In general, most of traditional potentials do not have this property.…”