Quantam Liénard II equation and Jacobi's Last Multiplier
In this survey the role of Jacobi's last multiplier in mechanical systems with a position dependent mass is unveiled. In particular, we map the Liénard II equation x" + f(x)x'2 + g(x) = 0 to a position dependent mass system. The quantization of the Liénard II equation is then carried...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2015-09-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v10/p10_01.pdf |
| _version_ | 1811273023739658240 |
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| author | A. Ghose Choudhury Partha Guha |
| author_facet | A. Ghose Choudhury Partha Guha |
| author_sort | A. Ghose Choudhury |
| collection | DOAJ |
| description | In this survey the role of Jacobi's last multiplier in mechanical systems with a position dependent mass is unveiled. In particular, we map the Liénard II equation x" + f(x)x'2 + g(x) = 0 to a position dependent mass system. The quantization of the Liénard II equation is then carried out using the point canonical transformation method together with the von Roos ordering technique. Finally we show how their eigenfunctions and eigenspectrum can be obtained in terms of associated Laguerre and exceptional Laguerre functions. By employing the exceptional Jacobi polynomials we construct three exactly solvable potentials giving rise to bound-state solutions of the Schrödinger equation. |
| first_indexed | 2024-04-12T22:50:44Z |
| format | Article |
| id | doaj.art-de17476c693b4ce08b7bd076c98a461c |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-04-12T22:50:44Z |
| publishDate | 2015-09-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-de17476c693b4ce08b7bd076c98a461c2022-12-22T03:13:21ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982015-09-0110 (2015)121Quantam Liénard II equation and Jacobi's Last MultiplierA. Ghose Choudhury0Partha Guha 1Department of Physics, Surendranath College, Mahatma Gandhi Road, Calcutta-700009, IndiaS. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata - 700098, IndiaIn this survey the role of Jacobi's last multiplier in mechanical systems with a position dependent mass is unveiled. In particular, we map the Liénard II equation x" + f(x)x'2 + g(x) = 0 to a position dependent mass system. The quantization of the Liénard II equation is then carried out using the point canonical transformation method together with the von Roos ordering technique. Finally we show how their eigenfunctions and eigenspectrum can be obtained in terms of associated Laguerre and exceptional Laguerre functions. By employing the exceptional Jacobi polynomials we construct three exactly solvable potentials giving rise to bound-state solutions of the Schrödinger equation.http://www.utgjiu.ro/math/sma/v10/p10_01.pdfLiénard II equationposition-dependent massJacobi last multiplierSchrödinger equationexceptional Laguerre equationexceptional Jacobi polynomial |
| spellingShingle | A. Ghose Choudhury Partha Guha Quantam Liénard II equation and Jacobi's Last Multiplier Surveys in Mathematics and its Applications Liénard II equation position-dependent mass Jacobi last multiplier Schrödinger equation exceptional Laguerre equation exceptional Jacobi polynomial |
| title | Quantam Liénard II equation and Jacobi's Last Multiplier |
| title_full | Quantam Liénard II equation and Jacobi's Last Multiplier |
| title_fullStr | Quantam Liénard II equation and Jacobi's Last Multiplier |
| title_full_unstemmed | Quantam Liénard II equation and Jacobi's Last Multiplier |
| title_short | Quantam Liénard II equation and Jacobi's Last Multiplier |
| title_sort | quantam lienard ii equation and jacobi s last multiplier |
| topic | Liénard II equation position-dependent mass Jacobi last multiplier Schrödinger equation exceptional Laguerre equation exceptional Jacobi polynomial |
| url | http://www.utgjiu.ro/math/sma/v10/p10_01.pdf |
| work_keys_str_mv | AT aghosechoudhury quantamlienardiiequationandjacobislastmultiplier AT parthaguha quantamlienardiiequationandjacobislastmultiplier |