Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching
In this paper, we present a derivation of the relativistic equations of Quantum Mechanics. We focus on the second order equations (both Klein Gordon’s and Dirac’s), since the linear Dirac equation can be derived from these. This derivation is an extension of the same method applied to the non-relati...
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Sociedade Brasileira de Física
2025-01-01
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| Series: | Revista Brasileira de Ensino de Física |
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| author | L.S.F. Olavo Marcello Ferreira |
| author_facet | L.S.F. Olavo Marcello Ferreira |
| author_sort | L.S.F. Olavo |
| collection | DOAJ |
| description | In this paper, we present a derivation of the relativistic equations of Quantum Mechanics. We focus on the second order equations (both Klein Gordon’s and Dirac’s), since the linear Dirac equation can be derived from these. This derivation is an extension of the same method applied to the non-relativistic case in a in a previous series of articles by us. We show that, to extend the theoretical framework to the relativistic case, we have only to extend the axioms in a relativistically compatible way, as should be the case with any extension of an axiomatic method. We also show that this quantization method throws light in a different way to interpret some descriptors of the usual formalism, mainly those regarding the expression for the probability density function. This, on the other hand, gives the teacher following this approach in classes on the subject to assess the epistemological issue of the role of manuals in the learning of Quantum Mechanics. |
| format | Article |
| id | doaj-art-b8508df270424f88aa9fe81b8046909d |
| institution | Kabale University |
| issn | 1806-9126 |
| language | Portuguese |
| publishDate | 2025-01-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj-art-b8508df270424f88aa9fe81b8046909d2025-02-04T07:38:00ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262025-01-014710.1590/1806-9126-rbef-2024-0426Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teachingL.S.F. Olavohttps://orcid.org/0000-0001-8078-3065Marcello Ferreirahttps://orcid.org/0000-0003-4945-3169In this paper, we present a derivation of the relativistic equations of Quantum Mechanics. We focus on the second order equations (both Klein Gordon’s and Dirac’s), since the linear Dirac equation can be derived from these. This derivation is an extension of the same method applied to the non-relativistic case in a in a previous series of articles by us. We show that, to extend the theoretical framework to the relativistic case, we have only to extend the axioms in a relativistically compatible way, as should be the case with any extension of an axiomatic method. We also show that this quantization method throws light in a different way to interpret some descriptors of the usual formalism, mainly those regarding the expression for the probability density function. This, on the other hand, gives the teacher following this approach in classes on the subject to assess the epistemological issue of the role of manuals in the learning of Quantum Mechanics.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172025000100602&lng=en&tlng=enSchrödinger equationRelativistic equationsMathematical derivationTeaching of quantum mechanics |
| spellingShingle | L.S.F. Olavo Marcello Ferreira Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching Revista Brasileira de Ensino de Física Schrödinger equation Relativistic equations Mathematical derivation Teaching of quantum mechanics |
| title | Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching |
| title_full | Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching |
| title_fullStr | Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching |
| title_full_unstemmed | Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching |
| title_short | Derivation of the Schrödinger equation V: Relativistic Equations of Quantum Mechanics and its epistemological impacts on teaching |
| title_sort | derivation of the schrodinger equation v relativistic equations of quantum mechanics and its epistemological impacts on teaching |
| topic | Schrödinger equation Relativistic equations Mathematical derivation Teaching of quantum mechanics |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172025000100602&lng=en&tlng=en |
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