The Particular Solution of the Equation of Motion of a Single Particle under Lennard-Jones Potential

Abstract

This research focuses on solving the particular solution of the equation of motion of a single particle under Leonard-Jones potential by defining the new parameter as x=(r/r_e )^-6. We found that the Leonard Jones potential becomes parabolic in shape with the turning point shifted to r =1.122r_e. There are appear two conditions at r=0 and r=r_e. We applied this potential to the Euler-Lagrange equation, it was found that the equation was similar to the equation of motion of harmonic oscillation. However, when defining the boundary conditions for arbitrary constants, the arbitrary constants are complicated form, meanwhile, the equation of motion and their particular solutions we got are in a form that is suitable for further application in calculated the classical action of the system to determine the propagator and the wavefunction by path integral method.