(20) 5. Conversion of two body problem into a one-body problem. Assume two particles of unequal mass interact through a potential V(r) that depends only on the distance between them and show how the Hamiltonians (both classical and quantum mechanical) governing their motion in 3D cartesian coordinates can be split into a Hamiltonian for the center of mass and a Hamiltonian for a particle with reduced mass. Hint:Use the figure and notation in the figure Chem 444 Problem Set \#5 Spring 2023 Page 2 below and convert to center of mass coordinates and relative coordinates r=R2R1:Rcm= (m1R1+m2R2)/(m1+m2) R1=Rcm+r1R2=Rcm+r2