A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM
Supersymmetric quantum mechanics has wide applications in physics. However, there are few potentials that can be solved exactly by supersymmetric quantum mechanics methods, so it is undoubtedly of great significance to find more potentials that can be solved exactly. This paper studies the supersymm...
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1593 |
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| author | Lulin Xiong Xin Tan Shikun Zhong Wei Cheng Guang Luo |
| author_facet | Lulin Xiong Xin Tan Shikun Zhong Wei Cheng Guang Luo |
| author_sort | Lulin Xiong |
| collection | DOAJ |
| description | Supersymmetric quantum mechanics has wide applications in physics. However, there are few potentials that can be solved exactly by supersymmetric quantum mechanics methods, so it is undoubtedly of great significance to find more potentials that can be solved exactly. This paper studies the supersymmetric quantum mechanics problems of the Schrödinger equation with a new kind of generalized trigonometric tangent superpotential: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>tan</mi><mi>n</mi><mi>p</mi><mi>x</mi><mo>+</mo><mi>B</mi><mi>tan</mi><mi>m</mi><mi>p</mi><mi>x</mi></mrow></semantics></math></inline-formula>. We will elaborate on this new potential in the following aspects. Firstly, the shape invariant relation of partner potential is generated by the generalized trigonometric tangent superpotential. We find three shape invariance forms that satisfy the additive condition. Secondly, the eigenvalues and the eigenwave functions of the potential are studied separately in these three cases. Thirdly, the potential algebra of such a superpotential is discussed, and the discussions are explored from two aspects: one parameter’s and two parameters’ potential algebra. Through the potential algebra, the eigenvalue spectrums are given separately which are consistent with those mentioned earlier. Finally, we summarize the paper and give an outlook on the two-parameter shape-invariant potential. |
| first_indexed | 2024-03-09T03:46:55Z |
| format | Article |
| id | doaj.art-e8d4dc13a158410791d875b65cc7c6d9 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:46:55Z |
| publishDate | 2022-08-01 |
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| spelling | doaj.art-e8d4dc13a158410791d875b65cc7c6d92023-12-03T14:33:01ZengMDPI AGSymmetry2073-89942022-08-01148159310.3390/sym14081593A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQMLulin Xiong0Xin Tan1Shikun Zhong2Wei Cheng3Guang Luo4College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, ChinaChongqing Fengjie Middle School, Chongqing 404699, ChinaCollege of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, ChinaCollege of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, ChinaCollege of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, ChinaSupersymmetric quantum mechanics has wide applications in physics. However, there are few potentials that can be solved exactly by supersymmetric quantum mechanics methods, so it is undoubtedly of great significance to find more potentials that can be solved exactly. This paper studies the supersymmetric quantum mechanics problems of the Schrödinger equation with a new kind of generalized trigonometric tangent superpotential: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>tan</mi><mi>n</mi><mi>p</mi><mi>x</mi><mo>+</mo><mi>B</mi><mi>tan</mi><mi>m</mi><mi>p</mi><mi>x</mi></mrow></semantics></math></inline-formula>. We will elaborate on this new potential in the following aspects. Firstly, the shape invariant relation of partner potential is generated by the generalized trigonometric tangent superpotential. We find three shape invariance forms that satisfy the additive condition. Secondly, the eigenvalues and the eigenwave functions of the potential are studied separately in these three cases. Thirdly, the potential algebra of such a superpotential is discussed, and the discussions are explored from two aspects: one parameter’s and two parameters’ potential algebra. Through the potential algebra, the eigenvalue spectrums are given separately which are consistent with those mentioned earlier. Finally, we summarize the paper and give an outlook on the two-parameter shape-invariant potential.https://www.mdpi.com/2073-8994/14/8/1593supersymmetric quantum mechanicsgeneralized trigonometric tangent superpotentialshape invariancepotential algebra |
| spellingShingle | Lulin Xiong Xin Tan Shikun Zhong Wei Cheng Guang Luo A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM Symmetry supersymmetric quantum mechanics generalized trigonometric tangent superpotential shape invariance potential algebra |
| title | A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM |
| title_full | A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM |
| title_fullStr | A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM |
| title_full_unstemmed | A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM |
| title_short | A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM |
| title_sort | new solvable generalized trigonometric tangent potential based on susyqm |
| topic | supersymmetric quantum mechanics generalized trigonometric tangent superpotential shape invariance potential algebra |
| url | https://www.mdpi.com/2073-8994/14/8/1593 |
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