Talk:Cubic harmonic

This page shows the Tesseral Harmonics, but not the Cubic (or Kubic?) Harmonics. Up to l=2 they only differ by the natural order of the basis functions, for l>=3 they are different linear combinations of the Spherical Harmonics. (Tesseral the combination Ylm and Yl-m, for Kubic (Cubic?) Harmonics they are the irreducible representations in the Cubic point-group (a1u, t1u and t2u for l=3).

Clearly, you are right. Either English has a funny convention in naming the real linear combinations of Spherical Harmonics (which are just Y(m) ± Y(-m)), or the title of the article is plainly wrong. While the s,p,d functions described here also adhere to cubic symmetry, the f’s do not; therefore, they should not be called “cubic”.

Just for the sake of completeness: The correct cubic linear combinations of f functions are xyz (A_2u), {x³, y³, z³} (T_1u; this is actually a shorthand) and {x(z²–y²), y(z²–x²), z(x²–y²)} (T_2u). In general, these cubic functions mix several different values of m together. — Preceding unsigned comment added by 117.205.137.175 (talk) 14:55, 20 August 2013 (UTC)

Fully agreed, These are the tesseral and not the cubic harmonics. I'm willing to modify the article and suggest a new page for tesseral harmonics if nobody objects. I would follow the definitions used here http://quanty.org/physics_chemistry/orbitals/start — Preceding unsigned comment added by Maurits W. Haverkort (talk • contribs) 07:58, 21 May 2020 (UTC)