On the general theory of bound state spectra in the Coulomb few- and many-body systems

Abstract

Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schrödinger equation written for arbitrary few- and many-particle Coulomb systems. The first approach is the matrix factorization method. Another method is based on the $D^{+}-$series of representations of the hyper-radial O(2,1)-algebra. The both these methods allow us to obtain the closed analytical formulas for the bound state energies in an arbitrary many-particle Coulomb system.

accepted for publication in Chem.Phys.Lett. (2018)

References in corpus (2)

• On the $Q$-dependence of the lowest-order QED corrections and other properties of the ground $1^{1}S-$states in the two-electron ions
• Matrix mechanics for actual atoms and molecules

Cited by in corpus (2)

• Mass-dependencies of the bound state properties for three-body positronium-like exitonic complexes
• Asymptotic and interpolation series for the Coulomb three-body systems with unit charges