Publication
Relativistic particle in a box: Klein–Gordon versus Dirac equations
| Summary: | The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein–Gordon equation in the Feshbach–Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect. |
|---|---|
| Main Authors: | Alberto, Pedro |
| Other Authors: | Das, Saurya; Vagenas, Elias C. |
| Subject: | Relativistic Particle in a Box |
| Year: | 2018 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade de Coimbra |
| Language: | English |
| Origin: | Estudo Geral - Universidade de Coimbra |
| _version_ | 1877780316665413632 |
|---|---|
| author | Alberto, Pedro |
| author2 | Das, Saurya Vagenas, Elias C. |
| author2_role | author author |
| author_facet | Alberto, Pedro Das, Saurya Vagenas, Elias C. |
| author_role | author |
| contributor_name_str_mv | Estudo Geral |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Alberto, Pedro\"},{\"Person.name\":\"Das, Saurya\"},{\"Person.name\":\"Vagenas, Elias C.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Estudo Geral |
| datacite.creators.creator.creatorName.fl_str_mv | Alberto, Pedro Das, Saurya Vagenas, Elias C. |
| datacite.date.Accepted.fl_str_mv | 2018-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2018-01-01T00:00:00Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Relativistic Particle in a Box |
| datacite.titles.title.fl_str_mv | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| dc.contributor.none.fl_str_mv | Estudo Geral |
| dc.creator.none.fl_str_mv | Alberto, Pedro Das, Saurya Vagenas, Elias C. |
| dc.date.Accepted.fl_str_mv | 2018-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2018-01-01T00:00:00Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/10316/84292 |
| dc.language.none.fl_str_mv | eng |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Relativistic Particle in a Box |
| dc.title.fl_str_mv | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein–Gordon equation in the Feshbach–Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | estudogl_b0fd69a411f3b072ee0d58c0ce1dad27 |
| identifier.url.fl_str_mv | https://hdl.handle.net/10316/84292 |
| inst_facet_str | urn:organizationAcronym:uc{{{_:::_}}}Universidade de Coimbra |
| instacron_str | uc |
| institution | Universidade de Coimbra |
| instname_str | Universidade de Coimbra |
| language | eng |
| network_acronym_str | estudogl |
| network_name_str | Estudo Geral - Universidade de Coimbra |
| oai_identifier_str | oai:estudogeral.uc.pt:10316/84292 |
| organization_str_mv | urn:organizationAcronym:uc |
| person_str_mv | Alberto, Pedro Das, Saurya Vagenas, Elias C. |
| publishDate | 2018 |
| repo_facet_str | urn:repositoryAcronym:estudogl{{{_:::_}}}Estudo Geral - Universidade de Coimbra |
| reponame_str | Estudo Geral - Universidade de Coimbra |
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| service_str_mv | urn:repositoryAcronym:estudogl |
| spelling | engengThe problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein–Gordon equation in the Feshbach–Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.application/pdfporRelativistic particle in a box: Klein–Gordon versus Dirac equationsAlberto, PedroDas, SauryaVagenas, Elias C.HostingInstitutionOrganizationalEstudo Gerale-mailmailto:inf@sib.uc.ptinf@sib.uc.ptDOIIsPartOf10.1088/1361-6404/aa9b432018-012018-01-01T00:00:00Z2018-01-01T00:00:00ZHandlehttps://hdl.handle.net/10316/84292http://purl.org/coar/access_right/c_abf2open accessRelativistic Particle in a Box162473 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articleapplication/pdfhttps://estudogeral.uc.pt/bitstream/10316/84292/1/ArXiv_1711.06313.pdf |
| spellingShingle | Relativistic particle in a box: Klein–Gordon versus Dirac equations Alberto, Pedro Relativistic Particle in a Box |
| status | SINGLETON |
| subject.fl_str_mv | Relativistic Particle in a Box |
| title | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| title_full | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| title_fullStr | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| title_full_unstemmed | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| title_short | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| title_sort | Relativistic particle in a box: Klein–Gordon versus Dirac equations |
| topic | Relativistic Particle in a Box |
| topic_facet | Relativistic Particle in a Box |
| url | https://hdl.handle.net/10316/84292 |
| visible | 1 |
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