Quantum Alchemy: Transmutation of Atomic Orbitals

• S. M. Blinder ^[1]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
• Localización: Journal of chemical education, ISSN 0021-9584, Vol. 78, Nº 3, 2001, pág. 391
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.