Determination of point group harmonics for arbitrary j by a projection method. I. Cubic group, quantization along an axis of order 4

We give a method for systematically building cubic harmonics, i.e., base vectors of irreducible representations of the group of invariance of a cube. Applications include solid state physics, molecular chemistry, spectroscopy, etc. The only necessary operators are Cz4 and Ry, rotation of π/2 around 0y. Projectors on representations are constructed; then their rows are orthogonalized by a Schmidt method and normalized simply by dividing by the square root of a diagonal element.