The hydrogen atom revisited

The One Dimensional Hydrogen Atom Revisited

The one dimensional Schrödinger hydrogen atom is an interesting mathematical and physical problem to study bound states, eigenfunctions and quantum degeneracy issues. This 1D physical system gave rise to some intriguing controversy over more than four decades. Presently, still no definite consensus seems to have been reached. We reanalyzed this apparently controversial problem, approaching it f...

Structure of the Hydrogen Atom

It was demonstrated recently[1] that the correct mathematical expression for the total energy H of a particle is H = mv, where m is the relativistic mass and v is the velocity; not H = mc as was widely believed. In this paper, the equation H = mv will be used to calculate the energy levels in the spectrum of the hydrogen atom. It is demonstrated that the well-known Sommerfeld-Dirac formula is s...

The 2-dimensional hydrogen atom

In these notes we investigate a particular partial differential equation arising from the quantum mechanical description of a hydrogen atom. For simplicity we consider the atom in a 2-dimensional instead of a 3-dimensional universe. For convenience we put all fundamental constants of nature equal to 1. The problem. In quantum mechanics the electron is described by a so called wave function. A w...

Hydrogen Atom-formaldehyde Reaction

where H-H-C and H-D-C are weak bonds and make a negligible contribution, leads to a value of -2 kcal. Therefore, E5-E2=1 kcal compared with the experimental value of 1.0 kcal. The preexponential factor for this pair of isotopic reactions can be calculated from the difference in the entropies of activation. Using the same loose complex as above and applying the expression derived by Bigeleisens ...

Fine Structure of the Hydrogen Atom.