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# final - PHYS 507 Quantum Mechanics I Final Examination...

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PHYS 507 Quantum Mechanics I Final Examination Assigned: January 2, 2006. Due: January 6, 2006, Friday, 16:00. Rules: As opposed to the homeworks, for the final exam you are not allowed to talk to your friends (or to anybody) about the exam. Solve all problems by yourself. If you share your solutions with your friends, I reserve the right to give you any letter grade I wish. All of the following problems can be solved from what you have learned in the class. You may consult any book you want, but this will be unnecessary. 1. The spin-orbit interaction in atoms couples the orbital angular momentum and spin of electrons by a term in the Hamiltonian of the form H = 2 ¯ h f ~ L · ~ S , where ~ L is the orbital angular momentum and ~ S is the spin of a particular electron. Actually, this is not the only term in the Hamiltonian. However, since we are going to ignore the radial motion of the electron below, we are going to treat H given above as the total Hamiltonian. Because of this, we are going to assume that f is a constant (in reality it depends on the radial coordinate of the electrons). The Hamiltonian given above then, gives us a fairly good idea for the angular and spin motion of the electron. Suppose that the electron is in a p -state ( = 1 where is the quantum number for the square of orbital angular momentum L 2 ).

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