Wolfram Alpha:
Search by keyword:
Astronomy
Chemistry
Classical Mechanics
Classical Physics
Climate Change
Cosmology
Finance and Accounting
Game Theory
General Relativity
Group Theory
Lagrangian and Hamiltonian Mechanics
Macroeconomics
Mathematics
Mathjax
Microeconomics
Nuclear Physics
Particle Physics
Probability and Statistics
Programming and Computer Science
Quantitative Methods for Business
Quantum Computing
Quantum Field Theory
Quantum Mechanics
Semiconductor Reliability
Solid State Electronics
Special Relativity
Statistical Mechanics
String Theory
Superconductivity
Supersymmetry (SUSY) and Grand Unified Theory (GUT)
The Standard Model
Topology
Units, Constants and Useful Formulas
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.