Two interacting particles in no external potential: a. two free particles of mass m and m move in 1d (on the x-axis) with an interaction between them that depends only on their separation, v(x -x2). write down the time-independent schroedinger equation for energy e and state ψ(x1, x2). b. rewrite the equation in terms of xthe center of mass x, and a/ax and ax. c. by separating variables, putting ψ-vr (x)wu(x), find the form ofvr (x) and show that ψ(x) satisfies the schroedinger equation for a single particle moving in a potential d. in 3d the same reduction to an effective one-particle problem occurs, so in hydrogen (a proton plus an electron) the motion of the nucleus can be accounted for. find the ratios of the binding energies of deuterium and hydrogen atoms (assume the deuterium nucleus mass is twice that of hydrogen)