Resumen de Quantum Alchemy: Transmutation of Atomic Orbitals
Hydrogen-like atomic orbitals can be transmuted among themselves using various mathematical transformations. Orbitals with the same (n,l ) are interrelated, more or less obviously, by geometry in 3-dimensional space. Those with the same n but different l are related by a "hidden symmetry" arising from the Runge-Lenz vector--originally an additional conserved quantity in planetary motion. Finally, different values of n can be generated by ladder operators acting on the radial functions. Collectively, these create an "alchemy" among atomic orbitals, which would have delighted the medieval alchemists! The splitting of the (n,l) degeneracy in many-electron atoms is analyzed in terms of the breakdown of commutativity of the Runge-Lenz vector with the Hamiltonian.
