Question

Consider two particles of mass m connected by a spring with rest length L with potential energy given by

V(x1, x2) = ½ k (x1 – x2 – L)2.

Show that the total wavefunction for this system is the product of two terms, one term is the solution for free particle motion of the center of mass for a particle with the total mass and the other term is simple harmonic (vibrational) motion of the relative displacement x1-x2 of the reduced mass. Find an expression for the energies of the stationary states of vibrational motion in terms of m and k. How do these results change if one particle has mass m and the other particle has mass 4m?

Answer 1