i want the solution of question 5.1 from:"introduction to quantom mechanics"(David J.Griffiths)?

Question

schrodinger equation for two particle system(in terms of reduced mass,center of mass,...)

schrodinger equation for two particle system(in terms of reduced mass,center of mass,...)I dont know how will change laplacian operatpor from particles normal coordinates,to center of mass and seperation coordinates.

Answer 1

Reduced mass=m1m2/(m1+m2); center of mass=(m1x1+m2x2)/(m1+m2). If r=the separation of the two particles with the CM as origin, then you can rewrite x1 and x2 in terms of r and the CM.

The resulting equation should split into two parts: one for the CM and one for the motion of the reduced mass relative to the CM.

Good luck.