# 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.

Each density-matrix element connects two states

s_{1} and

s_{2} (or one state with itself for the diagonal elements). The states are indicated with a subscript

StateLabel[s_{i}] 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.

Out[2]= | |

The density matrix for this system.

Out[3]//MatrixForm= |

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Density-matrix elements for systems with Zeeman structure have subscript

{StateLabel[s_{i}], M[s_{i}]} for each state

s_{i}.

An atomic system consisting of a

J=1 state and a

J=0 state.

Out[4]= | |

The density matrix for this system.

Out[5]//MatrixForm= |

| |

Density matrix elements for systems with hyperfine and Zeeman structure have subscripts

{StateLabel[s_{i}], F[s_{i}], M[s_{i}]} for each state.

An atomic system consisting of a

J=1/2 state in an atom with nuclear spin

I=1/2.

Out[6]= | |

The density matrix for this system.

Out[7]//MatrixForm= |

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