Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well
Abstract We discuss the influence of several factors on the deviations from energy spectrum of an infinite square quantum well (QW) for real microscopic systems that can be approximately modelled using particle in a box. We introduce the “blurring” potential in the form of the modified Woods-Saxon p...
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
2019-11-01
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| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100410&tlng=en |
| _version_ | 1798014969880510464 |
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| author | Vladimir Ivchenko |
| author_facet | Vladimir Ivchenko |
| author_sort | Vladimir Ivchenko |
| collection | DOAJ |
| description | Abstract We discuss the influence of several factors on the deviations from energy spectrum of an infinite square quantum well (QW) for real microscopic systems that can be approximately modelled using particle in a box. We introduce the “blurring” potential in the form of the modified Woods-Saxon potential and solve the corresponding Schrödinger equation. It is found that the increase of the degree of blurring δ of the QW leads to the increase of number of the energy levels inside it and to increase of deviations from the quadratic dependence ε (n) (ε is the particle energy, n is the energy level number) typical for the infinite square QW, especially, for the energy levels close to the QW “tops”. It is most surprising that for relatively “large” values of δ the difference between the levels energies of such well and the appropriate (with the same n) levels energies of the square QW with the same depth changes sign (from positive to negative) as number n increases. We also conclude that the asymmetry of the QW and non-equality m i n ≠ m o u t (where m i n and m o u t are the particle effective mass inside and outside the QW) play a significant role for the relatively “shallow” well near the QW top. |
| first_indexed | 2024-04-11T15:26:42Z |
| format | Article |
| id | doaj.art-57f138661a37464797c9797db2c2adab |
| institution | Directory Open Access Journal |
| issn | 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-04-11T15:26:42Z |
| publishDate | 2019-11-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-57f138661a37464797c9797db2c2adab2022-12-22T04:16:14ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262019-11-014210.1590/1806-9126-rbef-2019-0222Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square wellVladimir Ivchenkohttps://orcid.org/0000-0001-7367-3669Abstract We discuss the influence of several factors on the deviations from energy spectrum of an infinite square quantum well (QW) for real microscopic systems that can be approximately modelled using particle in a box. We introduce the “blurring” potential in the form of the modified Woods-Saxon potential and solve the corresponding Schrödinger equation. It is found that the increase of the degree of blurring δ of the QW leads to the increase of number of the energy levels inside it and to increase of deviations from the quadratic dependence ε (n) (ε is the particle energy, n is the energy level number) typical for the infinite square QW, especially, for the energy levels close to the QW “tops”. It is most surprising that for relatively “large” values of δ the difference between the levels energies of such well and the appropriate (with the same n) levels energies of the square QW with the same depth changes sign (from positive to negative) as number n increases. We also conclude that the asymmetry of the QW and non-equality m i n ≠ m o u t (where m i n and m o u t are the particle effective mass inside and outside the QW) play a significant role for the relatively “shallow” well near the QW top.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100410&tlng=eninfinite square quantum wellthe “blurring” potentialthe asymmetry of QWthe position-dependent effective mass |
| spellingShingle | Vladimir Ivchenko Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well Revista Brasileira de Ensino de Física infinite square quantum well the “blurring” potential the asymmetry of QW the position-dependent effective mass |
| title | Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well |
| title_full | Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well |
| title_fullStr | Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well |
| title_full_unstemmed | Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well |
| title_short | Quantitative analysis of the applicability limits of the model of a one-dimensional infinite square well |
| title_sort | quantitative analysis of the applicability limits of the model of a one dimensional infinite square well |
| topic | infinite square quantum well the “blurring” potential the asymmetry of QW the position-dependent effective mass |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172020000100410&tlng=en |
| work_keys_str_mv | AT vladimirivchenko quantitativeanalysisoftheapplicabilitylimitsofthemodelofaonedimensionalinfinitesquarewell |