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arXiv · 2507.20045

Symplectic Pauli-Schr\"odinger Equation for the Quark-Antiquark Interaction System

R. R. Luz·R. A. S. Paiva·G. X. A. Petronilo·A. E. Santana·T. M. Rocha Filho·R. G. G. Amorim
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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 Levi-Civita 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 transiet magnetic field measured in non-central heavy-ion collisions at RHIC and LHC.

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R. R. Luz, R. A. S. Paiva, G. X. A. Petronilo, A. E. Santana, T. M. Rocha Filho, R. G. G. Amorim. 2025-07-26. Symplectic Pauli-Schr\"odinger Equation for the Quark-Antiquark Interaction System. https://arxiv.org/abs/2507.20045

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