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Units, Constants and Useful Formulas

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Zeeman Effect
-------------

The magnetic dipole moment is given by:

μ = IA

The torque on the dipole moment is given by:

τ = μ x B

The torque tends to line up the magnetic
dipole moment with the magnetic field
because this represents the lowest energy
configuration.

The potential energy associated with the
dipole moment is:

U(θ) = -μ.B

Therefore, the change in energy between
the up and down state is:

ΔE = 2μB

The magnetic dipole moment for the
electron is:

μe = -eL/2m

Therefore the energy becomes:

E = eBL/2m

For the orbital angular momentum in
the z-direction,

L = ml.  Thus we can write:

E = ehBml/2m

= μBmlB

Where μB is the Bohr Magneton = eh/2m

This gives a displacement in the energy
levels such that:

ΔE = mlμBB

This splitting of the levels is referred
to as the ZEEMAN EFFECT.

Similarly, for the spin angular momentum,
MS = ±1/2h.  Thus, we can write:

E = ehBmS/2m

= μBmSB

In general, the Zeeman effect is the result
of both the orbital and spin angular momenta.
Thus, we can write:

ΔE = (e/2m)(L + gS).B = gLμBmJB

Where g is the spin g-factor ~ 2 and gL
is the LANDE g-factor

The Lande g-factor is a geometric factor
that compensates for the fact that the S
and L vectors are both precessing around
the magnetic field in generally different
directions.