>>11218857Define "exist".
No seriously, tell me. What do you mean by exist? Yes the mathematical functions "exist", in that I can write down an expression for Legendre polynomials which express a certain mathematical idea. Yes, they exist in that these functions solve a mathematical equation which expresses a model of nature which is a very good approximation to the quantitative measurements of nature we have made. Yes, they exist in the sense that, even though they do not diagonalize the "full" Hamiltonian of an atom (whatever the fuck that looks like), they are a complete orthonormal basis for and thus we can expand the atom's "true" eigenstates as a linear combination of them.
But I suspect you have some much more schizophrenic definition of "exist" which falls outside the purview of science as an endeavor.
