Czasopismo
2018
|
Vol. 24, No. 3
|
177--185
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
In this work, aiming to solve numerically the Schrödinger equation with a Dirac delta function potential, we use the Numerov method to solve the time independent 1D-Schrödinger equation with potentials of the form V (x) + αβp(x), where δp(x) is a pseudo-delta function, a very high and thin barrier. The numerical results show good agreement with analytical results found in the literature. Furthermore, we show the numerical solutions of a system formed by three delta function potentials inside of an infinite quantum well and the harmonic potential with position dependent mass and a delta barrier in the center.
Słowa kluczowe
Rocznik
Tom
Strony
177--185
Opis fizyczny
Bibliogr. 11 poz., rys.
Twórcy
autor
- Federal Institute of Education, Science and Technology of Ceara, Fortaleza-Ce, Brazil, samueldgm@fisica.ufc.br
autor
- Lab. of Quantum Information Technology, Department of Teleinformatic Engineering Federal University of Ceara - DETI/UFC, C.P. 6007 – Campus do Pici, 60455-970 Fortaleza-Ce, Brazil, rubens.ramos@ufc.br
Bibliografia
- [1] J.J. Álvarez, M. Gadella, F.J.H. Heras, L.M. Nieto, A onedimensional model of resonances with a delta barrier and mass jump, Phys. Lett. A 373, 4022–4027 (2009).
- [2] F.M. Toyama, Y. Nogami, Transmission-reflection problem with a potential of the form of the derivative of the delta function, J. Phys. A: Math. Theor. 40, F685–F690 (2007).
- [3] A.V. Zolotaryuk, Y. Zolotaryuk, Controllable resonant tunneling through single-point potentials: A point triode, Phys. Lett. A 379, 511–517 (2015).
- [4] A.V. Zolotaryuk, Boundary conditions for the states with resonant tunnelling across the δ’-potential, Phys. Lett. A 374, 1636–1641 (2010).
- [5] M. Belloni, R.W. Robinett, The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics, Phys. Rep. 540, 25–122 (2014).
- [6] M. Pillai, J. Goglio, T.G. Walker, Matrix Numerov method for solving Schrödinger’s equation, Am. J. Phys., 80, 11, 1017–1019, 2012.
- [7] P. Pedram, M. Vahabi, Exact solutions of a particle in a box with a delta function potential: The factorization method, Am. J. Phys. 78, 8, 839–841 (2010).
- [8] D.J. Griffiths, Introduction to Quantum Mechanics, 2nd Edition; Pearson Education Chapter 2, 2005. Available online in http://physicspages.com/2012/08/21/infinite-squarewell-with-delta-function-barrier.
- [9] O. von Roos, Position-dependent effective masses in semiconductor theory, Phys. Rev. B 27, 7547 (1983).
- [10] A. Ganguly, ¸ S. Kuru, J. Negro, L.M. Nieto, A study of the bound states for square potential wells with position-dependent mass, Phys. Lett. A 360, 228–233 (2006).
- [11] S.D.G. Martinz, R.V. Ramos, Double quantum well triple barrier structures: analytical and numerical results, Can. J. Phys. 94, 11, 1180–1188 (2016).
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-48d83ba7-79f5-43d4-b63e-a010dddc0a14