3. It was demonstrated in class that the operators , have the remarkable properties of "raising""lowering" given state to the one up/down: 1., 1 1.H ) = CIL.# + 1). Ill.H) = DIL.H-1) (1) where C and D are constants. What are they? 1. Operator of the angular momentum of two particles of masses m, 2 has the form 1=1, +h=-ir, x Vil-ir, x V21 (1 ) where r, 2 are position vectors of the particles while V1 2 refers to vector differentiation with respect to coordinates of particles 1 or 2. Introducing the relative position vector (2) and the center of mass vector R mir+ m252 (3) mi + my show that the total angular momentum (1) can be presented as a sum of the angular momentum of the relative motion, and the angular momentum of the translational motion of the entire system as a whole. Your answer should be given in terms of r. R and corresponding differential operators V, and VR- 5. (a) The dipole moment of a system of charged particles (for example, an atom) is given by the expression d = Zer. where a labels the particles, e, are their charges while r, are their radius vectors. Show that in a state characterized by definite parity the average dipole moment is zero. Can an elementary particle have a finite dipole moment? W Q Search