Exact Classical Quantum-Mechanical Solutions for One- through Twenty-Electron Atoms

摘要

It is true that the Schrodinger equation can be solved exactly for the hydrogen atom, although it is not true that the result is the exact solution of the hydrogen atom. Electron spin is missed entirely, and there are many internal inconsistencies and nonphysical consequences that do not agree with experimental results. The Dirac equation does not reconcile this situation. Many additional shortcomings arise, such as instability to radiation, negative kinetic energy states, intractable infinities, virtual particles at every point in space, the Klein paradox, violation of Einstein causality, and "spooky " action at a distance. Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive physical reality has widened. The connection between QM and reality is more than just a "philosophical" issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as a physical as opposed to a purely mathematical "tool. " Some of these issues are discussed in a review by Laloe [Am. J. Phys. 69, 655 (2001)]. But QM has severe limitations even as a tool. Beyond one-electron atoms, multielectron-atom quantum-mechanical equations cannot be solved except by approximation methods involving adjustable-parameter theories (perturbation theory, variational methods, self-consistent field method, multicon-figuration Hartree-Fock method, multiconfiguration parametric potential method, 1/Z expansion method, multiconfiguration Dirac-Fock method, electron correlation terms, QED terms, etc.), all of which contain assumptions that cannot be physically tested and are not consistent with physical laws. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e" moving in the Coulombic field of the proton and the wave equation as modified after Schrodinger, a classical, approach was explored, yielding a model that is remarkably accurate and provides insight into physics on the atomic level [R.L. Mills, Phys. Essays 16, 433 (2003); 17, 342 (2004); The Grand Unified Theory of Classical Quantum Mechanics (BlackLight Power, Inc., Cranbury, NJ, 2005)]. Physical laws and intuition are restored when dealing with the wave equation and quantum-mechanical problems.