4. The chain rule is a useful method for transferring from cee set of coordinates to another. In solving the Harmonic Oxcillator we took the 6 degrees of freedom associated with 2 atoms and rodoced is to 1 coordinate, the relative motion of two anoms on their linc of center throagh the center of mass. However, it is useful to do the actual transformation using the chain rule. A^rot=A^Cu+A^Vn using the chain rale. For example, x1=x1xx+x1xxx1=m1+m1xxx22=(x)2 Ete. A^cu=f(x,Y,z)=2M2CN2AVE=f(x,y,z)=2x2VW2+V(xyz) Assume V(x1x2)V(xyz) as derivatives are not involved. Note: In class when we deal witb rotation we will further transform A^Car(xyz) to AVA(r) which is a much more complex transformation. We won't do the details, cnly give the