More generally, see also the Laplace-Beltrami and Laplace-de Rham operators, both defined on (pseudo-)Riemannian manifolds not necessarily embedded in ℝ³.
Even more generally, see the huge body of beautiful mathematics that has arisen from the study of elliptic differential operators in general (de Rham cohomology, Hodge theory, the Atiyah-Singer index theorem, …).
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That’s a very quantum physics-centric explanation though (username checks out…).
A more general definition is that they are eigenfunctions of the Laplacian operator on a sphere, which arise in many contexts.
More generally, see also the Laplace-Beltrami and Laplace-de Rham operators, both defined on (pseudo-)Riemannian manifolds not necessarily embedded in ℝ³.
Even more generally, see the huge body of beautiful mathematics that has arisen from the study of elliptic differential operators in general (de Rham cohomology, Hodge theory, the Atiyah-Singer index theorem, …).