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SIGMA, 2007, том 3, 067, 14 страниц (Mi sigma193)  

Эта публикация цитируется в 48 научных статьях (всего в 48 статьях)

Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions

Christiane Quesne

Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium

Аннотация: An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations.

Ключевые слова: Schrödinger equation; position-dependent mass; quadratic algebra

DOI: https://doi.org/10.3842/SIGMA.2007.067

Полный текст: PDF файл (251 kB)
Полный текст: http://emis.mi.ras.ru/.../067
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: 0705.2577
Тип публикации: Статья
MSC: 81R12; 81R15
Поступила: 30 марта 2007 г.; в окончательном варианте 8 мая 2007 г.; опубликована 17 мая 2007 г.
Язык публикации: английский

Образец цитирования: Christiane Quesne, “Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions”, SIGMA, 3 (2007), 067, 14 pp.

Цитирование в формате AMSBIB
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\paper Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schr\"odinger Equation in Two Dimensions
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Quesne C., “Spectrum generating algebras for position-dependent mass oscillator Schrödinger equations”, J. Phys. A, 40:43 (2007), 13107–13119  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Kalnins E.G., Miller W. (Jr.), Post S., “Wilson polynomials and the generic superintegrable system on the 2-sphere”, J. Phys. A, 40:38 (2007), 11525–11538  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. E. G. Kalnins, Willard Miller. Jr., Sarah Post, “Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D”, SIGMA, 4 (2008), 008, 21 pp.  mathnet  crossref  mathscinet  zmath
    4. Bagchi B., Tanaka T., “A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models”, Phys. Lett. A, 372:33 (2008), 5390–5393  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Sever R., Tezcan C., Yeşiltaş Ö., Bucurgat M., “Exact solution of effective mass Schrodinger equation for the Hulthen potential”, Internat. J. Theoret. Phys., 47:9 (2008), 2243–2248  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Tezcan C., Sever R., Yeşiltaş Ö., “A new approach to the exact solutions of the effective mass Schrödinger equation”, Internat. J. Theoret. Phys., 47:6 (2008), 1713–1721  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Quesne C., “Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass”, J. Math. Phys., 49:2 (2008), 022106, 15 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. C. Quesne, “Quadratic algebras and position-dependent mass Schrodinger equations”, 5th International Symp. on Quantum Theory and Symmetries, Journal of Physics: Conference Series, 128, 2008, 012059  crossref  adsnasa  isi  scopus
    9. Marquette I., “Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials”, J. Math. Phys., 50:9 (2009), 095202, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Arda A., Sever R., “Approximate $l$-state solutions to the Klein-Gordon equation for modified Woods-Saxon potential with position dependent mass”, Internat. J. Modern Phys. A, 24:20-21 (2009), 3985–3994  crossref  mathscinet  zmath  adsnasa  isi
    11. Midya B., Roy B., “A generalized quantum nonlinear oscillator”, J. Phys. A, 42:28 (2009), 285301, 18 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    12. Kalnins E.G., Miller W., Post S., “Models of quadratic quantum algebras and their relation to classical superintegrable systems”, Physics of Atomic Nuclei, 72:5 (2009), 801–808  crossref  adsnasa  isi  scopus
    13. Marquette I., “Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials”, J. Math. Phys., 50:1 (2009), 012101, 23 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Arda A., Sever R., Tezcan C., “Approximate analytical solutions of the Klein-Gordon equation for the Hulthen potential with the position-dependent mass”, Phys. Scr., 79:1 (2009), 015006, 5 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Kalnins E.G., Miller W. (Jr.), Post S., “Coupling constant metamorphosis and $N$th-order symmetries in classical and quantum mechanics”, J. Phys. A, 43:3 (2010), 035202, 20 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Lee Yu.-H., Yang W.-L., Zhang Ya.-Zh., “Polynomial algebras and exact solutions of general quantum nonlinear optical models: II. Multi-mode boson systems”, Journal of Physics A-Mathematical and Theoretical, 43:37 (2010), 375211  crossref  mathscinet  zmath  isi  scopus
    17. Kalnins E.G., Miller W. Jr., Post S., “Models for the 3D Singular Isotropic Oscillator Quadratic Algebra”, Phys Atomic Nuclei, 73:2 (2010), 359–366  crossref  adsnasa  isi  elib  scopus
    18. Lee Yu.-H., Yang W.-L., Zhang Ya.-Zh., “Polynomial algebras and exact solutions of general quantum nonlinear optical models I: two-mode boson systems”, Journal of Physics A-Mathematical and Theoretical, 43:18 (2010), 185204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Sarah Post, “Models of Quadratic Algebras Generated by Superintegrable Systems in 2D”, SIGMA, 7 (2011), 036, 20 pp.  mathnet  crossref  mathscinet
    20. Marquette I., “Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators”, Journal of Physics A-Mathematical and Theoretical, 44:23 (2011), 235203  crossref  mathscinet  zmath  adsnasa  isi  scopus
    21. Marquette I., “Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems”, J Math Phys, 52:4 (2011), 042301  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. Grandati Y., Berard A., Mohrbach H., “On Peres approach to Fradkin-Bacry-Ruegg-Souriau's perihelion vector”, Central European Journal of Physics, 9:1 (2011), 88–95  crossref  adsnasa  isi  scopus
    23. Yannis Tanoudis, Costas Daskaloyannis, “Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler–Coulomb Potential”, SIGMA, 7 (2011), 054, 11 pp.  mathnet  crossref  mathscinet
    24. Arda A., Sever R., “Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass”, Commun Theor Phys (Beijing), 56:1 (2011), 51–54  crossref  mathscinet  zmath  adsnasa  isi  scopus
    25. Ikhdair S.M., “Effective Schrodinger Equation with General Ordering Ambiguity Position-Dependent MASS Morse Potential”, Mol. Phys., 110:13 (2012), 1415–1428  crossref  adsnasa  isi  elib  scopus
    26. Bojowald M., Kempf A., “Generalized Uncertainty Principles and Localization of a Particle in Discrete Space”, Phys. Rev. D, 86:8 (2012), 085017  crossref  mathscinet  adsnasa  isi  elib  scopus
    27. Marquette I., “Generalized Five-Dimensional Kepler System, Yang-Coulomb Monopole, and Hurwitz Transformation”, J. Math. Phys., 53:2 (2012), 022103  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    28. Menculini L., Panella O., Roy P., “Exact Solutions of the (2+1) Dimensional Dirac Equation in a Constant Magnetic Field in the Presence of a Minimal Length”, Phys. Rev. D, 87:6 (2013), 065017  crossref  adsnasa  isi  elib  scopus
    29. Miller Jr. Willard Post S. Winternitz P., “Classical and Quantum Superintegrability with Applications”, J. Phys. A-Math. Theor., 46:42 (2013), 423001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    30. Panahi H. Alizadeh Z., “Deformed Oscillator Algebra for Quantum Superintegrable Systems in Two-Dimensional Euclidean Space and on a Complex Two-Sphere”, Chin. Phys. B, 22:6 (2013), 060304  crossref  adsnasa  isi  elib  scopus
    31. Marquette I., “Quartic Poisson Algebras and Quartic Associative Algebras and Realizations as Deformed Oscillator Algebras”, J. Math. Phys., 54:7 (2013), 071702  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    32. Isaac Ph.S. Marquette I., “On Realizations of Polynomial Algebras with Three Generators via Deformed Oscillator Algebras”, J. Phys. A-Math. Theor., 47:20 (2014), 205203  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    33. Rajbongshi H., Singh N.N., “Generation of New Exactly Solvable Potentials of Position-Dependent Mass Schrodinger Equation By Extended Transformation Method”, Acta Phys. Pol. B, 45:8 (2014), 1701–1712  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    34. Li Ya., Zhang F.-L., Gu R.-J., Chen J.-L., Kwek L.C., “Constructing Physical Systems With Dynamical Symmetry”, Can. J. Phys., 92:4 (2014), 335–340  crossref  adsnasa  isi  elib  scopus
    35. Aghaei S. Chenaghlou A., “Solution of the Dirac Equation With Some Superintegrable Potentials By the Quadratic Algebra Approach”, Int. J. Mod. Phys. A, 29:6 (2014), 1450028  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    36. Х. Райбонгши, Н. Н. Сингх, “Построение точно решаемых потенциалов в $D$-мерном уравнении Шредингера с массой, зависящей от координат, при помощи метода преобразований”, ТМФ, 183:2 (2015), 312–328  mathnet  crossref  mathscinet  adsnasa  elib; H. Rajbongshi, N. N. Singh, “Generation of exactly solvable potentials of the $D$-dimensional position-dependent mass Schrödinger equation using the transformation method”, Theoret. and Math. Phys., 183:2 (2015), 715–729  crossref  isi
    37. Nikitin A.G. Zasadko T.M., “Superintegrable Systems With Position Dependent Mass”, J. Math. Phys., 56:4 (2015), 042101  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    38. Aghaei S., Chenaghlou A., “Quadratic Algebra Approach To the Dirac Equation With Spin and Pseudospin Symmetry For the 4D Harmonic Oscillator and U(1) Monopole”, Few-Body Syst., 56:1 (2015), 53–61  crossref  adsnasa  isi  scopus
    39. Х. Райбонгши, “Точно решаемые потенциалы и решения для связанных состояний уравнения Шредингера в $D$-мерном пространстве с зависящей от координат массой”, ТМФ, 184:1 (2015), 117–133  mathnet  crossref  mathscinet  adsnasa  elib; H. Rajbongshi, “Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space”, Theoret. and Math. Phys., 184:1 (2015), 996–1010  crossref  isi
    40. Mohammadi V., Aghaei S., Chenaghlou A., “Klein-Gordon Equation With Superintegrable Systems: Kepler-Coulomb, Harmonic Oscillator, and Hyperboloid”, Adv. High. Energy Phys., 2015, 701042  crossref  mathscinet  zmath  isi  scopus
    41. Evnin O., Nivesvivat R., “AdS Perturbations, Isometries, Selection Rules and the Higgs Oscillator”, J. High Energy Phys., 2016, no. 1, 151  crossref  mathscinet  zmath  isi  elib  scopus
    42. Ioffe M.V. Kolevatova E.V. Nishnianidze D.N., “SUSY method for the three-dimensional Schr?dinger equation with effective mass”, Phys. Lett. A, 380:41 (2016), 3349–3354  crossref  mathscinet  zmath  isi  elib  scopus
    43. Nikitin A.G. Zasadko T.M., “Group classification of Schr?dinger equations with position dependent mass”, J. Phys. A-Math. Theor., 49:36 (2016), 365204  crossref  mathscinet  zmath  isi  elib  scopus
    44. Mohammadi V., Aghaei S., Chenaghlou A., “Dirac equation in presence of the Hartmann and Higgs oscillator superintegrable potentials with the spin and pseudospin symmetries”, Int. J. Mod. Phys. A, 31:35 (2016), 1650190  crossref  mathscinet  zmath  isi  elib  scopus
    45. Evnin O., Nivesvivat R., “Hidden Symmetries of the Higgs Oscillator and the Conformal Algebra”, J. Phys. A-Math. Theor., 50:1 (2017), 015202  crossref  mathscinet  zmath  isi  scopus
    46. Ioffe M.V., Nishnianidze D.N., Vereshagin V.V., “Mapping of Two-Dimensional Schrodinger Equation Under the Point Transformation”, J. Math. Phys., 58:7 (2017), 072105  crossref  mathscinet  zmath  isi  scopus
    47. Moussa M.H., Merad M., “Relativistic Oscillators in Generalized Snyder Model”, Few-Body Syst., 59:3 (2018), UNSP 44  crossref  isi  scopus
    48. Rajbongshi H., “Exact Analytic Solution of Position-Dependent Mass Schrodinger Equation”, Indian J. Phys., 92:3 (2018), 357–367  crossref  isi  scopus
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