Fundamental Theoretical Difference in Ground-state Spectra of 2-electron Systems bound by Coulomb and Harmonic Potentials

Authors

• Viraht Sahni, CUNY Brooklyn CollegeFollow
• Marlina Slamet, Sacred Heart University

Document Type

Article

Publication Date

2026

Abstract

We note a fundamental difference in the theoretically obtained ground-state spectra of 2-electron systems bound by the Coulomb and Harmonic potentials. The Coulomb bound systems considered are the natural Helium atom, Hydrogen molecule and Tri Hydrogen cation. The 'artificial' Harmonic bound systems are the 2D semiconductor quantum dot in a magnetic field with the electron spin moment and its interaction with the magnetic field considered, 3D Hooke’s atom, 3D Hooke’s molecule and 3D Tri Harmonic Oscillator cation. Experiment and theory confirm the ground state of natural systems is solely a singlet state. We prove that for the ‘artificial’ systems in the Wigner high-electron-correlation regime, there is associated with the ground singlet state, a ground triplet state identified by its replication of theoretical ground state characteristics of correlated systems. The proof is via exact, analytical, correlated wave function solutions of the corresponding Schrödinger-Pauli/Schrödinger equations for both the ground singlet and triplet states.

Comments

This is the authors' accepted manuscript of an article originally published in International Journal of Quantum Chemistry, available at https://doi.org/10.1002/qua.70268