ps7 - Physics 212 – Problem Set 7 – Spring 2010 1. The...

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Unformatted text preview: Physics 212 – Problem Set 7 – Spring 2010 1. The Zeeman Effect with Nuclear Spin An external magnetic field is applied to a system with nuclear spin I and electron total spin J . The zeroth order Hamiltonian then gains the term H(1) = AI · J − µJ · B − µI · B. Applying the magnetic field in the z direction yields ˆ H(1) = AI · J + gJ µB Jz Bz − gI µB Iz Bz , where µJ = gJ µB J and µI = gI µB I define the new g-factors. Consider a system where the nuclear spin i=3 (like Boron 10) and the electron total spin j =3/2 (for instance, an electron in a p state). Calculate the shifts in the energy levels caused by H(1) in (a) the weak field limit: A >> gJ µB Bz , and (b) the strong field limit: A << gJ µB Bz . (c) Sketch the energy level diagram, showing the movement of the levels in energy versus the strength of the magnetic field. Take gI ∼ 0. On the left will be your weak field results, on the right the strong field results, and in between schematic sketches indicating how the levels connect. 2. C-TDL Ch. 13 problem 1 3. C-TDL Ch. 13 problem 2 4. C-TDL Ch. 13 problem 3 5. C-TDL Ch. 13 problem 5 1 ...
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