Charge quadrupole operators (Q)
The quadrupole operator is a special case of the crystal-field operator. The operator is defined as: Qij=3rirj/r2−ˆr⋅ˆrδi,j. Whereby we need to note that we here only take the angular part of a quadrupole. It's “strength”, i.e. the expectation value of r2 is omitted from our definition.