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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.20045 |
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| _version_ | 1866912850745753600 |
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| author | Luz, R. R. Paiva, R. A. S. Petronilo, G. X. A. Santana, A. E. Filho, T. M. Rocha Amorim, R. G. G. |
| author_facet | Luz, R. R. Paiva, R. A. S. Petronilo, G. X. A. Santana, A. E. Filho, T. M. Rocha Amorim, R. G. G. |
| contents | 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-Schrödinger-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cornell Interaction in the Two-body Pauli-Schrödinger-type Equation Framework: The Symplectic Quantum Mechanics Formalism Luz, R. R. Paiva, R. A. S. Petronilo, G. X. A. Santana, A. E. Filho, T. M. Rocha Amorim, R. G. G. Quantum Physics High Energy Physics - Theory 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-Schrödinger-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. |
| title | Cornell Interaction in the Two-body Pauli-Schrödinger-type Equation Framework: The Symplectic Quantum Mechanics Formalism |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.20045 |