Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics
In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solv...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/3409776 |
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| author | Renato Luz Gustavo Petronilo Ademir de Santana Caroline Costa Ronni Amorim Rendisley Paiva |
| author_facet | Renato Luz Gustavo Petronilo Ademir de Santana Caroline Costa Ronni Amorim Rendisley Paiva |
| author_sort | Renato Luz |
| collection | DOAJ |
| description | In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the cc¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space. |
| format | Article |
| id | doaj-art-4e2317353c934ce592f91161b577bcf8 |
| institution | Kabale University |
| issn | 1687-7365 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-4e2317353c934ce592f91161b577bcf82025-02-03T05:57:09ZengWileyAdvances in High Energy Physics1687-73652022-01-01202210.1155/2022/3409776Quark-Antiquark Effective Potential in Symplectic Quantum MechanicsRenato Luz0Gustavo Petronilo1Ademir de Santana2Caroline Costa3Ronni Amorim4Rendisley Paiva5International Center of PhysicsInternational Center of PhysicsInternational Center of PhysicsInstituto de Física TeóricaInternational Center of PhysicsInternational Center of PhysicsIn this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the cc¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space.http://dx.doi.org/10.1155/2022/3409776 |
| spellingShingle | Renato Luz Gustavo Petronilo Ademir de Santana Caroline Costa Ronni Amorim Rendisley Paiva Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics Advances in High Energy Physics |
| title | Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics |
| title_full | Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics |
| title_fullStr | Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics |
| title_full_unstemmed | Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics |
| title_short | Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics |
| title_sort | quark antiquark effective potential in symplectic quantum mechanics |
| url | http://dx.doi.org/10.1155/2022/3409776 |
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