The standard operators as used in Quanty require one to define a basis set for the orbitals. Most (but not all) standard operators implemented assume an atomic shell with spherical symmetry. The spin-orbitals are then given by a radial wave-function times a function depending on the angular coordinates: $\psi(x,y,z)=R(r)\Theta(\theta,\phi)$. The program uses by default the complex spherical harmonics ($Y$) for the angular part, but one can change this and use either the Tesseral Harmonics ($Z$), Kubic Harmonics ($K$) or a basis of $j-j_z$ coupled spin-orbitals ($j$) with an option to the operator definitions. (Note that this freedom in basis choice is great as it allows good flexibility, but also requires the user to make sure all definitions are consistent. The sum of two operators on a different basis is quite meaningless.) Here we briefly list the orbital basis sets we use and the order and phase we take. Note further that one can always define an operator on a given basis and rotate it later to an other basis.

Note that the use of a basis of spherical harmonics times a radial basis function for the orbital is quite common and does not restrict one selves to only solutions where the final eigen-states need to be spherical. It's just the basis. For example Gaussian based DFT codes have a basis of spherical harmonics (tesseral harmonics) times a radial basis function (Gaussian).