Quantum three body Coulomb problem in two dimensions

Details Quantum three body Coulomb problem in two dimensions Quantum three body Coulomb problem in two dimensions

2002-03-29

arxiv.org/abs/quant-ph/0203150v2

Physics

Quantum Physics

27 pages, 3 figures. submitted to PRA

Scientific paper

10.1103/PhysRevA.66.022101

We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using annihilation and creation operators of four harmonic oscillators, coupled by various terms of degree up to twelve. We analyse in details the discrete symmetry properties of the eigenstates. The energy levels and eigenstates of the two-dimensional helium atom are obtained numerically, by expanding the Schr\"{o}dinger equation on a convenient basis set, that gives sparse banded matrices, and thus opens up the way to accurate and efficient calculations. We give some very accurate values of the energy levels of the first bound Rydberg series. Using the complex coordinate method, we are also able to calculate energies and widths of doubly excited states, i.e. resonances above the first ionization threshold. For the two-dimensional $H^{-}$ ion, only one bound state is found.

Affiliated with

Also associated with

No associations

Rating

Quantum three body Coulomb problem in two dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum three body Coulomb problem in two dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum three body Coulomb problem in two dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-240643