Cornell Interaction in the Two-body Pauli-Schr\"odinger-type Equation Framework: The Symplectic Quantum Mechanics Formalism
Abstract
We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and non-confining interactions. After performing a Bohlin mapping in phase space, we solve the time-independent symplectic Pauli-Schr\"odinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark, that is revealed in the phase space structure. Due to the presence of spin in the Hamiltonian, the results reveal that the magnetic field enhances the non-classicality of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The experimental mass spectra is used to estimate the intensity of the external field, leading to a value that is in order of the transient magnetic field measured in non-central heavy-ion collisions at RHIC and LHC.
Keywords
Cite
@article{arxiv.2507.20045,
title = {Cornell Interaction in the Two-body Pauli-Schr\"odinger-type Equation Framework: The Symplectic Quantum Mechanics Formalism},
author = {R. R. Luz and R. A. S. Paiva and G. X. A. Petronilo and A. E. Santana and T. M. Rocha Filho and R. G. G. Amorim},
journal= {arXiv preprint arXiv:2507.20045},
year = {2026}
}
Comments
15 pages, 3 figures, and 1 table