2009midterm - NAME: MIDTERM EXAM PHYS852 Quantum Mechanics...

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Unformatted text preview: NAME: MIDTERM EXAM PHYS852 Quantum Mechanics II, Spring 2009 1. [50 pts] Consider a system of two spin-1/2 particles, with corresponding spin operators, vector S 1 , and vector S 2 . They do not interact with each other, but they both interact with a spin-1 particle, with spin operator vector I . Let the bare Hamiltonian for the system be H = 2 planckover2pi1 bracketleftBig vector S 1 vector I + vector S 2 vector I bracketrightBig a.) [10 pts] Let vector S = vector S 1 + vector S 2 . What are the allowed values of the quantum number s ? For each s what are the possible m s values? b.) [10 pts] Let the total angular momentum operator be vector F = vector S + vector I . For each possible s-value, give the allowed values of the quantum number f . For each state with well-defined s and f , list the possible m f values. c.) [10 pts] What are the eigenvalues of H ? For each eigenvalue, give the degeneracy factor, and list the corresponding degenerate states....
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2009midterm - NAME: MIDTERM EXAM PHYS852 Quantum Mechanics...

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