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
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
Relaxation and Repopulation
IntrinsicRelaxation relaxation matrix for spontaneous decay
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
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
Basic Examples
Advanced Examples
Copyright and License:
Copyright (C) 2004—2018 Simon M. Rochester <>
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