AtomicDensityMatrix Package
AtomicDensityMatrix is a package for Mathematica version 6+ that facilitates density-matrix calculations in atomic and related systems.
Note: The documentation is incomplete; there may be missing symbol reference pages. Look at the tutorials to get started. Documentation is currently an active part of package development.
Atomic Systems
AtomicState — expression representing an atomic state
Sublevels — generate the hyperfine and Zeeman sublevels for a list of atomic states
J  ▪ L  ▪ S  ▪ M  ▪ NuclearSpin  ▪ F  ▪ Energy  ▪ HyperfineA  ▪ HyperfineB  ▪ NaturalWidth  ▪ GFactor  ▪ StateLabel  ▪ BranchingRatio  ▪ Parity  ▪ AtomicSystemQ  ▪ AtomicSystemType  ▪ StatePosition  ▪ SelectStates  ▪ DeleteStates  ▪ ExcitedStates  ▪ GroundStates  ▪ RemoveZeemanSublevels
Atomic Properties
AtomicData — spectroscopic data for a selection of atomic states
Density Matrices and State Vectors
DensityMatrix — create density matrix for an atomic system
DMVariables  ▪ Ket
Operators and Hamiltonians
WignerEckart — matrix elements of spherical tensor operators
Hamiltonian — the Hamiltonian for an atomic system subject to external classical fields
RotatingWaveApproximation — perform the rotating-wave approximation on a Hamiltonian
RotatingWaveTransformMatrix  ▪ EffectiveHamiltonian
Relaxation and Repopulation
IntrinsicRelaxation — relaxation matrix for spontaneous decay
TransitRelaxation  ▪ TransitRepopulation
Atomic Evolution
LiouvilleEquation — evolution equations for an atomic system
InitialConditions — specify the density matrix at an initial time
Light Propagation
OpticalField — generate the expression for an optical field
Observables — the change in optical parameters upon propagation through an optically thin medium
LinearAbsorption — formula for absorption of weak light
Visualization
LevelDiagram — draw a level diagram for an atomic system, Hamiltonian, and density matrix
AMPSPlot — draw the angular-momentum probability surface for a density matrix
Tensor Algebra
ToCartesian — convert a spherical tensor into the Cartesian basis
Decomposition — decompose a reducible operator into a sum of polarization moments
Recomposition  ▪ TensorForm
TUTORIALS
Introduction
Components
Basic Examples
Advanced Examples
MORE ABOUT
Copyright and License:
Copyright (C) 2004—2018 Simon M. Rochester <simon@rochesterscientific.com>
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.