Variational bounds on the ground-state energy of three electrons and one hole in two-dimension

2000/12/31 by Nie Luo, Luo, Nie
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Spectral Theory in Mathematical Physics #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el

paper · pdf · doi:10.48550/arxiv.cond-mat/0101004

38 pages, 6 figures

openalex publication_date 2000/12/31 · arxiv created 2001/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of ≈ -0.0112me⁴/8π² ε² ℏ ² for the ground-state energy of such a system when the particles are near one another. The possible connections of such a complex to other fields of physics are discussed.

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