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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
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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