Quantum, classical and semiclassical momentum distributions: II. Morse and Coulomb potentials

Abstract

The basic properties of momentum distributions in quantum mechanics for elementary systems as well as their (semi-)classical analogue derived in a preceding paper are illustrated by a detailed analysis of the Morse oscillator and the three-dimensional Coulomb potential, where the distributions can be calculated in closed form.

Fisher information of D-dimensional hydrogenic systems in position and momentum spaces

“…20͒, and ͑iv͒ they play a very relevant role in numerous other physical processes with atoms and molecules which are governed by simple functions of the momentum transfer. 21,22 Moreover, the D-dimensional hydrogenic orbitals are of interest as manyelectron Sturmians. 23,24 For further details and motivation see Refs.…”

Quantum, classical and semiclassical momentum distributions: I. Theory and elementary examples

“…Here we confined ourselves to very elementary, but nonetheless instructive examples. In a companion paper, paper II [14], we will illustrate the properties of the quantum momentum distributions by a detailed discussion of two important examples, an anharmonic onedimensional potential (the Morse oscillator) and the three-dimensional Coulomb potential, where the distributions can be evaluated in closed form.…”

“…As instructive examples, we present a detailed discussion of very elementary special cases allowing a closed form solution in momentum space: Free and uniformly accelerating wave packets (section 3), the harmonic oscillator (section 4) and the square well (section 5). In a companion paper, part II [14], we discuss more elaborate applications, namely the anharmonic Morse oscillator and the Coulomb potential as an example in three dimensions.…”

Creation and fusion of photons

“…With this knowledge, we can relate the frequencies (ν e and ν γ ) of the electron and maximum-energy-photon (i.e., the one that leaves the atom). This relationship w is not directly dependent on angular momentum [18]. It depends on the resonance of the electron and photon frequencies.…”