Frustating use of the Laplace transform for the quantum states of a particle in a box
Abstract In a recent paper diffused in the literature, the quantum problem of a particle in a infinite square well potential was claimed to be solved via Laplace transform. Surprisingly, the correct solutions were found for an eigenvalue problem with variable defined on a finite range. As a matter o...
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
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| Series: | Revista Brasileira de Ensino de Física |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100436&lng=en&tlng=en |
| _version_ | 1818030053531844608 |
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| author | Antonio S. de Castro |
| author_facet | Antonio S. de Castro |
| author_sort | Antonio S. de Castro |
| collection | DOAJ |
| description | Abstract In a recent paper diffused in the literature, the quantum problem of a particle in a infinite square well potential was claimed to be solved via Laplace transform. Surprisingly, the correct solutions were found for an eigenvalue problem with variable defined on a finite range. As a matter of fact, the authors have misused the Laplace transform of the time-independent Schrödinger equation, and they have also used incorrectly the inversion process. In the present paper it is pointed out carefully and clearly those mistakes that might occur with the use of inappropriate methods for a given eigenvalue problem. |
| first_indexed | 2024-12-10T05:29:28Z |
| format | Article |
| id | doaj.art-fd1ed5e0a1d441e286cd9dfedfd78fe3 |
| institution | Directory Open Access Journal |
| issn | 1806-1117 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-12-10T05:29:28Z |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-fd1ed5e0a1d441e286cd9dfedfd78fe32022-12-22T02:00:37ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-11171806-91264210.1590/1806-9126-rbef-2020-0079S1806-11172020000100436Frustating use of the Laplace transform for the quantum states of a particle in a boxAntonio S. de CastroAbstract In a recent paper diffused in the literature, the quantum problem of a particle in a infinite square well potential was claimed to be solved via Laplace transform. Surprisingly, the correct solutions were found for an eigenvalue problem with variable defined on a finite range. As a matter of fact, the authors have misused the Laplace transform of the time-independent Schrödinger equation, and they have also used incorrectly the inversion process. In the present paper it is pointed out carefully and clearly those mistakes that might occur with the use of inappropriate methods for a given eigenvalue problem.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100436&lng=en&tlng=eninfinite square-well potentialparticle in a boxlaplace transform |
| spellingShingle | Antonio S. de Castro Frustating use of the Laplace transform for the quantum states of a particle in a box Revista Brasileira de Ensino de Física infinite square-well potential particle in a box laplace transform |
| title | Frustating use of the Laplace transform for the quantum states of a particle in a box |
| title_full | Frustating use of the Laplace transform for the quantum states of a particle in a box |
| title_fullStr | Frustating use of the Laplace transform for the quantum states of a particle in a box |
| title_full_unstemmed | Frustating use of the Laplace transform for the quantum states of a particle in a box |
| title_short | Frustating use of the Laplace transform for the quantum states of a particle in a box |
| title_sort | frustating use of the laplace transform for the quantum states of a particle in a box |
| topic | infinite square-well potential particle in a box laplace transform |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100436&lng=en&tlng=en |
| work_keys_str_mv | AT antoniosdecastro frustatinguseofthelaplacetransformforthequantumstatesofaparticleinabox |