Orientation of dumbbell

[mmvdwiel]

If alpha is larger than 0, we should have 2cos^2(theta)-sin^2(theta)>0 and as large as possible to have the minimal energy. This means the calculatinn of the maximum of 2-3sin^2(theta), so theta = 0 or pi, so the dumbbell is parallel or anti-parallel to the z-axis.
If alpha is zero, there will be no quadrupole energy, so all oriëntations will have the same energy.
If alpha is smaller than zero, we need to find the minimal energy configuration by finding the minimum of 2-3sin^2(theta), which lay at pi/2 and 3 pi/2, so the dumbbell has to be perpendicular to the z axis.

[Author]

Posts