Hydrogen atom from the standpoint of matrix mechanics

The model of the hydrogen atom originally introduced by Erwin Schrödinger in 1926 isa two-body proton -electron system. It relies on the Schrödinger operator H and on thelinear Schr¨odinger time dependent equation. Then Niels Bohr discovered that the modelcontradicts the basic dynamics of the atom and quantum wave mechanics was invented,with incidences here told from a deconstructive standpoint. The final section of this papersketches a new, alternative, continuous, causal and fully deterministic wave mechanics—already mentioned in [1], [2], [3] and elsewhere— crucially relying on H and solvablein terms of its eigenvalues and eigenfunctions, but definitely non-linear. An importantimplication is that the deterministic hydrogen atom must be conceived as a three-bodysystem consisting of proton, electron and photon.The model of the hydrogen atom originally introduced by Erwin Schrödinger in 1926 isa two-body proton -electron system. It relies on the Schrödinger operator H and on thelinear Schr¨odinger time dependent equation. Then Niels Bohr discovered that the modelcontradicts the basic dynamics of the atom and quantum wave mechanics was invented,with incidences here told from a deconstructive standpoint. The final section of this papersketches a new, alternative, continuous, causal and fully deterministic wave mechanics—already mentioned in [1], [2], [3] and elsewhere— crucially relying on H and solvablein terms of its eigenvalues and eigenfunctions, but definitely non-linear. An importantimplication is that the deterministic hydrogen atom must be conceived as a three-bodysystem consisting of proton, electron and photon.

Nov 14, 20210 citations

Quantum Mechanics of the Hydrogen Atom

Hermann Haken, Hans Christoph Wolf

Advanced texts in physicsJan 1, 20000 citations

Symmetry of a Hydrogen Atom in a Weak Magnetic Field

Sadaaki Yanagawa

The degeneracy problem of a hydrogen atom in a uniform weak magnetic field $H$ is considered from the standpoint of the invariance group that the system obeys. Evidently the degeneracy space has a constant $z$ component of the angular momentum. Under such a classification, the dynamical invariance of the problem is shown to be an isomorph to the Lie group of the linear transformation of the straight line.The degeneracy problem of a hydrogen atom in a uniform weak magnetic field $H$ is considered from the standpoint of the invariance group that the system obeys. Evidently the degeneracy space has a constant $z$ component of the angular momentum. Under such a classification, the dynamical invariance of the problem is shown to be an isomorph to the Lie group of the linear transformation of the straight line.

Physical Review AJul 1, 19737 citations

The degeneracy problem of a hydrogen atom in a uniform weak magnetic field

H

is considered from the standpoint of the invariance group that the system obeys. Evidently the degeneracy space has a constant

z

component of the angular momentum. Under such a classification, the dynamical invariance of the problem is shown to be an isomorph to the Lie group of the linear transformation of the straight line.