Angular-Momentum Probability Surfaces

The angular-momentum probability surface can be used as a graphical representation of the density matrix for a state with a particular total-angular-momentum quantum number.
MaxProjectionProbability[dm,,]probability of finding the maximum possible projection of angular momentum along direction (,) for density matrix dm
AMPSPlot[dm]plot the angular-momentum probability surface

Plotting angular-momentum probability surfaces.

This loads the package.
In[1]:=
Click for copyable input
Here is the formula for the angular-momentum probability surface for an aligned state.
In[2]:=
Click for copyable input
Out[2]=
Plot the surface using SphericalPlot3D.
In[3]:=
Click for copyable input
Out[3]=
AMPSPlot can be used to plot the surface directly. Axes3D adds axes to the plot.
In[4]:=
Click for copyable input
Out[4]=
AMPSPlot will also plot the probability surface for a density matrix expressed as a tensor decomposition.
In[5]:=
Click for copyable input
Out[5]=
In[6]:=
Click for copyable input
Out[6]=