English

Born-Oppenheimer Approximation for a Singular System

Mathematical Physics 2016-03-30 v2 High Energy Physics - Theory math.MP

Abstract

We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction. It is natural to apply Born-Oppenheimer approximation to this problem. We present a detailed discussion of this approach, the advantage of this simple model is that one can estimate the error terms self-consistently. Moreover, a Fock space approach to this problem is presented where a systematic expansion can be proposed to get higher order corrections. A slight modification of the same problem in which the light particle is relativistic is discussed in a later section. Here, the second quantized description is more challenging but with some care one can recover the first order term as well as introducing a more systematic approach to higher orders.

Keywords

Cite

@article{arxiv.1602.02811,
  title  = {Born-Oppenheimer Approximation for a Singular System},
  author = {Haci Akbas and O. Teoman Turgut},
  journal= {arXiv preprint arXiv:1602.02811},
  year   = {2016}
}

Comments

Some typos and minor errors are corrected, 37 pages, no figures

R2 v1 2026-06-22T12:46:06.150Z