B2) Consider a particle of mass M constrained to move on a sphere of radius R. Its Hamiltonian is 2MR? À where 2 = +2, +

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B2 Consider A Particle Of Mass M Constrained To Move On A Sphere Of Radius R Its Hamiltonian Is 2mr A Where 2 2 1 (42.29 KiB) Viewed 270 times

B2) Consider a particle of mass M constrained to move on a sphere of radius R. Its Hamiltonian is 2MR? À where 2 = +2, + 7, is the square of the orbital angular momentum operator with Cartesian components 1, 2, and î, a) Calculate the eigenvalues of , and specify their degeneracy. [3 marks) 2 b) A weak perturbation HM - MR (C.-C.). À where a«l, is added to . Assuming that the particle is in the state with orbital angular momentum quantum number 1=1, use degenerate perturbation theory to calculate the energies of the particle to first order in the perturbation [19 marks) c) Calculate the energies of the particle with Hamiltonian À = #, +,22 where 2 #12 - MR (7,+E). when it is in a state with orbital angular momentum quantum number 1 = 2. [8 marks) ?