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Method for Numerical Solution of the Stationary Schrödinger Equation

  • ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY
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Russian Physics Journal Aims and scope

The aim of this work is to describe a method of numerical solution of the stationary Schrödinger equation based on the integral equation that is identical to the Schrödinger equation. The method considered here allows one to find the eigenvalues and eigensolutions for quantum-mechanical problems of different dimensionality. The method is tested by solving problems for one-dimensional and two-dimensional quantum oscillators, and results of these tests are presented. Satisfactory agreement of the results obtained using this numerical method with well-known analytical solutions is demonstrated.

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References

  1. L. D. Landau and E. M. Lifshitz, Non-Relativistic Theory, Pergamon Press, Oxford (1977).

    MATH  Google Scholar 

  2. R. N. Kesarwani and Y. P. Varshni, J. Math. Phys., 22, No. 9, 1983–1989 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  3. V. V. Ul’yanov, Integral Methods in Quantum Mechanics [in Russian], Vishcha Shkola, Khar’kov (1982).

  4. C. M. Bender and T. T. Wu, Phys. Rev., 7, No. 6, 1620–1636 (1973).

    ADS  Google Scholar 

  5. J. P. Killingbeck, Microcomputer Quantum Mechanics, Adam Hilger, Bristol (1983).

    MATH  Google Scholar 

  6. K. Banerjee, S. P. Bhatnagar, and S. S. Kanwal, Proc. R. Soc. Bond., 360, 575–586 (1978).

    Article  ADS  Google Scholar 

  7. V. A. Cherkasskii, Visnyk Kharkivs’kogo Natsional’nogo Universitetu, No. 926, 204–211 (2010).

  8. M. Dineykhan and G. V. Efimov, Rep. Math. Phys., 6, No. 2/3, 287–308 (1995).

    Article  ADS  Google Scholar 

  9. A. G. Abrashkevich, D. G. Abrashkevich, and M. S. Kaschiev, Comp. Phys. Commun., 85, 65–74 (1995).

    Article  ADS  Google Scholar 

  10. M. Jafarpour and D. Afshar, J. Phys.: Math. Gen., A35, 87–92 (2002).

    ADS  Google Scholar 

  11. G. V. Kvitko, É. L. Kuzin, and D. V. Shot’, Vestnik Baltiiskogo Munitsipal’nogo Instituta Im. I. Kanta, No. 5, 115–119 (2011).

  12. A. N. Luk’yanenko and N. A. Chekanov, Voprosy Sovremennoi Nauki i Praktiki. Universitet Im. V. I. Vernadskogo, 2, No. 3(13), 43–49 (2008).

  13. A. D. Polyanin, Handbook on Linear Equations of Mathematical Physics [in Russian], Fizmatlit, Moscow (2001).

    MATH  Google Scholar 

  14. V. S. Vladimirov and V. V. Zharinov, Equations of Mathematical Physics: Textbook for Higher Education Institutions [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

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Authors and Affiliations

  1. Don State Technical University, Rostov-on-Don, Russia

    S. Yu. Knyazev & E. E. Shcherbakova

Authors
  1. S. Yu. Knyazev
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  2. E. E. Shcherbakova
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Correspondence to S. Yu. Knyazev.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–92, October, 2016.

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Knyazev, S.Y., Shcherbakova, E.E. Method for Numerical Solution of the Stationary Schrödinger Equation. Russ Phys J 59, 1616–1622 (2017). https://doi.org/10.1007/s11182-017-0953-6

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  • DOI: https://doi.org/10.1007/s11182-017-0953-6

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