PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2005 | 3 | 4 | 591-609
Tytuł artykułu

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.
Wydawca

Czasopismo
Rocznik
Tom
3
Numer
4
Strony
591-609
Opis fizyczny
Daty
wydano
2005-12-01
online
2005-12-01
Twórcy
  • Department of Mathematics, Swiss Federal Institute of Technology Zürich (ETH), ETH-Zentrum HG E 18.4, CH-8092, Zürich, Switzerland, xbat@math.ethz.ch
Bibliografia
  • [1] T. Gora and F. Williams: “Electronic states of homogeneous and inhomogeneous mixed semiconductors”, In: D.G. Thomas (Ed.):II–VI Semiconducting Compounds, Benjamin, New York, 1967.
  • [2] T. Gora and F. Williams: “Theory of electronic states and transport in graded mixed semiconductors”, Phys. Rev., Vol. 177, (1969), pp. 1179–1182. http://dx.doi.org/10.1103/PhysRev.177.1179[Crossref]
  • [3] G.T. Landsberg:Solid state theory: methods and applications, Wiley-Interscience, London, 1969.
  • [4] O. von Roos: “Position-dependent effective masses in semiconductor theory”, Phys. Rev. B, Vol. 27, (1983), pp. 7547–7552. http://dx.doi.org/10.1103/PhysRevB.27.7547[Crossref]
  • [5] O. von Roos and H. Mavromatis: “Position-dependent effective masses in semiconductor theory. II”, Phys. Rev. B, Vol. 31, (1985), pp. 2294–2298. http://dx.doi.org/10.1103/PhysRevB.31.2294[Crossref]
  • [6] J.-M. Lévy-Leblond: “Position-dependent effective mass and Galilean invariance”, Phys. Rev. A, Vol. 52(3), (1995), pp. 1845–1849. http://dx.doi.org/10.1103/PhysRevA.52.1845[Crossref]
  • [7] L. Dekar, L. Chetouani and T.F. Hammann: “An exactly soluble Schrödinger equation with smooth position-dependent mass”, J. Math. Phys., Vol. 39, (1998), pp. 2551–2563. http://dx.doi.org/10.1063/1.532407[Crossref]
  • [8] Á. de Souza Dutra and C.A.S. Almeida: “Exact solvability of potentials with spatially dependent effective masses”, Phys. Lett. A, Vol. 275, (2000), pp. 25–30. http://dx.doi.org/10.1016/S0375-9601(00)00533-8[Crossref]
  • [9] A.D. Alhaidari: “Solutions of the nonrelativistic wave equation with position-dependent effective mass”, Phys. Rev. A, Vol. 66, (2002), pp. 042116. http://dx.doi.org/10.1103/PhysRevA.66.042116[Crossref]
  • [10] B. Gönül, B. Gönül, D. Tutcu and O. Özer: “Supersymmetric approach to exactly solvable systems with position-dependent effective masses”, Modern Phys. Lett. A, Vol. 17, (2002), pp. 2057–2066. http://dx.doi.org/10.1142/S0217732302008563[Crossref]
  • [11] R. Koç and M. Koca: “A systematic study on the exact solution of the position dependent mass Schrödinger equation”, J. Phys. A, Vol. 36, (2003), pp. 8105–8112. http://dx.doi.org/10.1088/0305-4470/36/29/315[Crossref]
  • [12] J. Yu. Dong, S.-H. Dong and G.-H. Sun: “Series solutions of the Schrödinger equation with position-dependent mass for the Morse potential”, Phys. Lett. A., Vol. 322, (2004), pp. 290–297. http://dx.doi.org/10.1016/j.physleta.2004.01.039[Crossref]
  • [13] C. Quesne and V.M. Tkachuk: “Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem”, J. Phys. A, Vol. 37, (2004), pp. 4267–4281. http://dx.doi.org/10.1088/0305-4470/37/14/006[Crossref]
  • [14] Y.C. Ou, Z. Cao and Q. Shen: “Energy eigenvalues for the systems with position-dependent effective mass”, J. Phys. A, Vol. 37, (2004), pp. 4283–4288. http://dx.doi.org/10.1088/0305-4470/37/14/007[Crossref]
  • [15] G. Chen and Z.-D. Chen: “Exact solutions of the position-dependent Schrödinger equation in D dimensions”, Phys. Lett. A, Vol. 331, (2004), pp. 312–315. http://dx.doi.org/10.1016/j.physleta.2004.09.012[Crossref]
  • [16] A. Jannussis, G. Karayannis, P. Panagopoulos, V. Papatheou, M. Symeonidis, D. Vavougios, P. Siafarikas and V. Zisis: “Exactly soluble harmonic oscillator for a particular form of time and coordinates-dependent mass”, J. Phys. Soc. Japan, Vol. 53, (1984), pp. 957–962. http://dx.doi.org/10.1143/JPSJ.53.957[Crossref]
  • [17] A. Schulze-Halberg: “Form-preserving transformations of the time-dependent Schrödinger equation with time- and position-dependent mass”, Commun. Theor. Phys. (Beijing), Vol. 43, (2005), pp. 657–665. http://dx.doi.org/10.1088/0253-6102/43/4/017[Crossref]
  • [18] F. Finkel, A. Gonzalez-Lopez, N. Kamran and M.A. Rodriguez: “On form-preserving transformations for the time-dependent Schrodinger equation”, J. Math. Phys., Vol. 40, (1999), pp. 3268–3274. http://dx.doi.org/10.1063/1.532885[Crossref]
  • [19] M. Znojil (Ed.): “Proceedings of the 1st international workshop: pseudo-hermitian Hamiltonians in quantum physics”, Czech. J. Phys., Vol. 54, (2004), pp. 1–156.
  • [20] Á.de Souza Dutra, M.B. Hott and V.G.C.S. dos Santos: “Non-Hermitian time-dependent quantum systems with real energies”, quant-ph/0311044.
  • [21] G.T. Einevoll and P.C. Hemmer: “The effective-mass Hamiltonian for abrupt heterostructures”, J. Phys. C, Vol. 21, (1988), pp. L1193-L1198. http://dx.doi.org/10.1088/0022-3719/21/36/001[Crossref]
  • [22] G.T. Einevoll, P.C. Hemmer and J. Thomsen: “Operator ordering in effectivemass theory for heterostructures. I. Comparison with exact results for superlattices, quantum wells, and localized potentials”, Phys. Rev. B, Vol. 42, (1990), pp. 3485–3496. http://dx.doi.org/10.1103/PhysRevB.42.3485[Crossref]
  • [23] G.T. Einevoll: “Operator ordering in effective-mass theory for heterostructures. II. Strained systems”, Phys. Rev. B, Vol. 42, (1990), pp. 3497–3502. http://dx.doi.org/10.1103/PhysRevB.42.3497[Crossref]
  • [24] R.A. Morrow and K.R. Brownstein: “Model effective-mass Hamiltonians for abrupt heterojunctions and the associated wave-function-matching conditions”, Phys. Rev. B, Vol. 30, (1984), pp. 678–680. http://dx.doi.org/10.1103/PhysRevB.30.678[Crossref]
  • [25] R.A. Morrow: “Establishment of an effective-mass Hamiltonian for abrupt heterojunctions”, Phys. Rev. B, Vol. 35, (1987), pp. 8074–8079. http://dx.doi.org/10.1103/PhysRevB.35.8074[Crossref]
  • [26] J. Thomsen, G.T. Einevoll and P.C. Hemmer: “Operator ordering in effective-mass theory”, Phys. Rev. B, Vol. 39, (1989), pp. 12783–12788. http://dx.doi.org/10.1103/PhysRevB.39.12783[Crossref]
  • [27] Q.-G. Zhu and H. Kroemer: “Interface connection rules for effective-mass wave functions at an abrupt heterojunction between two different semiconductors”, Phys. Rev. B, Vol. 27, (1983), pp. 3519–3527. http://dx.doi.org/10.1103/PhysRevB.27.3519[Crossref]
  • [28] K.C. Yung and J.H. Yee: “Derivation of the modified Schrödinger equation for a particle with a spatially varying mass through path integrals”, Phys. Rev. A, Vol. 50, (1994), pp. 104–106. http://dx.doi.org/10.1103/PhysRevA.50.104[Crossref]
  • [29] E. Kamke:Differentialgleichungen-Lösungsmethoden und Lösungen, B.G. Teubner, Stuttgart, 1983.
  • [30] L. Dekar, L. Chetouani and T.F. Hammann: “Wave function for smooth potential and mass step”, Phys. Rev. A, Vol. 59, (1999), pp. 107–112. http://dx.doi.org/10.1103/PhysRevA.59.107[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02475615
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.