Displaying the Density Matrix

When an atomic system has been specified, its corresponding symbolic density matrix can be formed. This is done with the DensityMatrix function.

DensityMatrix[sys]form the density matrix for an atomic system
DMVariables[sys]form the list of variables representing density matrix elements

Forming the density matrix.

This loads the package.

Each density-matrix element connects two states s1 and s2 (or one state with itself for the diagonal elements). The states are indicated with a subscript StateLabel[si] for each state. For systems that take into account angular momentum, the angular-momentum quantum numbers are used as additional subscripts.

A two-level atomic system without angular momentum.
The density matrix for this system.

Density-matrix elements for systems with Zeeman structure have subscript {StateLabel[si], M[si]} for each state si.

An atomic system consisting of a J=1 state and a J=0 state.
The density matrix for this system.

Density matrix elements for systems with hyperfine and Zeeman structure have subscripts {StateLabel[si],F[si],M[si]} for each state.

An atomic system consisting of a J=1/2 state in an atom with nuclear spin I=1/2.
The density matrix for this system.