Dispersion of Klauder's temporally stable coherent states for the hydrogen atom

We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasi-classically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.Comment: 6 pages, 2 figure

Hydrogen atom in phase space: The Wigner representation

We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.Comment: 8 pages (including figures

Chemical Reaction between Single Hydrogen Atom and Graphene

We study chemical reaction between a single hydrogen atom and a graphene, which is the elemental reaction between hydrogen and graphitic carbon materials. In the present work, classical molecular dynamics simulation is used with modified Brenner's empirical bond order potential. The three reactions, that is, absorption reaction, reflection reaction and penetration reaction, are observed in our simulation. Reaction rates depend on the incident energy of the hydrogen atom and the graphene temperature. The dependence can be explained by the following mechanisms: (1) The hydrogen atom receives repulsive force by pi-electrons in addition to nuclear repulsion. (2) Absorbing the hydrogen atom, the graphene transforms its structure to the ``overhang'' configuration such as sp-3 state. (3) The hexagonal hole of the graphene is expanded during the penetration of the hydrogen atom.Comment: 10 pages, 9 figures. This paper was submitted to PR

The hydrogen atom in electric and magnetic fields : Pauli's 1926 article

The results obtained by Pauli, in his 1926 article on the hydrogen atom, made essential use of the dynamical so(4) symmetry of the bound states. Pauli used this symmetry to compute the perturbed energy levels of an hydrogen atom in a uniform electric field (Stark effect) and in uniform electric and magnetic fields. Although the experimental check of the single Stark effect on the hydrogen atom has been studied experimentally, Pauli's results in mixed fields have been studied only for Rydberg states of rubidium atoms in crossedfields and lithium atoms in parallel fields.Comment: 11 pages, latex file, 2 figure

Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable

We construct the most general SO(4,2) hydrogen atom coherent states which are the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We show that these states cannot be localized and cannot follow the classical orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent states is unattainable.Comment: 10 pages, report