Numerical Solution via Numerov Method of the 1D-Schrödinger Equation with Pseudo-Delta Barrier

• Autorzy: Martinz S. D. G. , Ramos R. V.

Identyfikatory

DOI

10.12921/cmst.2018.0000017

• Języki publikacji: EN

Abstrakty

EN

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

EN

Schrödinger equation; Numerov method; Dirac delta function potential

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2018
• Tom: Vol. 24, No. 3
• Strony: 177--185
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Martinz S. D. G.

• Federal Institute of Education, Science and Technology of Ceara, Fortaleza-Ce, Brazil

autor

Ramos R. V.

• 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

Bibliografia

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• [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.
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• [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).