Algorithms for Non-Relativistic Quantum Integral Equation
In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave...
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| Format: | Article |
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Universidade Federal de Viçosa (UFV)
2021-07-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/12699 |
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| author | Jorge Henrique de Oliveira Sales Pedro Henrique Sales Girotto |
| author_facet | Jorge Henrique de Oliveira Sales Pedro Henrique Sales Girotto |
| author_sort | Jorge Henrique de Oliveira Sales |
| collection | DOAJ |
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In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave that comes out after the particle collides with the scattering center. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. The methods used here are arbitrary kernels and the Neumann-Born series. The result, with the help of computational codes, shows that both techniques are good compared to the traditional method. The advantage is that they are finite solutions, which does not require Podolsky-type regularization.
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| format | Article |
| id | doaj-art-bdbc416b98994d329a7bdafbcb3c7483 |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2021-07-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-bdbc416b98994d329a7bdafbcb3c74832025-02-02T19:56:58ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752021-07-017310.18540/jcecvl7iss3pp12699-01-19eAlgorithms for Non-Relativistic Quantum Integral EquationJorge Henrique de Oliveira Sales0Pedro Henrique Sales Girotto1Universidade Estadual de Santa Cruz, DCET/ PPGMCCentro Universitario do Estado do Pará In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave that comes out after the particle collides with the scattering center. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. The methods used here are arbitrary kernels and the Neumann-Born series. The result, with the help of computational codes, shows that both techniques are good compared to the traditional method. The advantage is that they are finite solutions, which does not require Podolsky-type regularization. https://periodicos.ufv.br/jcec/article/view/12699Quantum scattering. Fredholm. Neumann-Born. Computational modeling. |
| spellingShingle | Jorge Henrique de Oliveira Sales Pedro Henrique Sales Girotto Algorithms for Non-Relativistic Quantum Integral Equation The Journal of Engineering and Exact Sciences Quantum scattering. Fredholm. Neumann-Born. Computational modeling. |
| title | Algorithms for Non-Relativistic Quantum Integral Equation |
| title_full | Algorithms for Non-Relativistic Quantum Integral Equation |
| title_fullStr | Algorithms for Non-Relativistic Quantum Integral Equation |
| title_full_unstemmed | Algorithms for Non-Relativistic Quantum Integral Equation |
| title_short | Algorithms for Non-Relativistic Quantum Integral Equation |
| title_sort | algorithms for non relativistic quantum integral equation |
| topic | Quantum scattering. Fredholm. Neumann-Born. Computational modeling. |
| url | https://periodicos.ufv.br/jcec/article/view/12699 |
| work_keys_str_mv | AT jorgehenriquedeoliveirasales algorithmsfornonrelativisticquantumintegralequation AT pedrohenriquesalesgirotto algorithmsfornonrelativisticquantumintegralequation |