Skip to main content
SpringerLink
Log in

An analysis of the exactly solvable linear differential equations by the Modified Airy Function (MAF) method

  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

Appropriate second order Linear Differential Equations (LDEs) which can be solved exactly by the Modified Airy Function (MAF) method, which normally gives approximate solutions in terms of Airy functions for Schrodinger-like LDEs, have been studied in three possible cases according to the MAF theory. The results of the exactly solvable LDEs have been classified in terms of two different family of LDEs with turning point and/or singular point parameter, one of which being a new class other than the known Time Independent Schrodinger’s Equation (TISE) with a linear potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R E Langer Trans. Am. Math. Soc. 33 23 (1931)

    Article  Google Scholar 

  2. A K Ghatak, R L Gallawa and I C Goyal Modified Airy Functions and WKB Solutions to the Wave Equation (Washington: NIST) (1991)

    Google Scholar 

  3. A K Ghatak, R L Gallawa, and I C Goyal IEE J. Quant. Electron. 28 400 (1992)

    Article  ADS  Google Scholar 

  4. I C Goyal, Sukhdev Roy, A K Ghatak and R L Gallawa Can. J. Phys. 70 1218 (1992)

    Article  ADS  Google Scholar 

  5. S Roy, I C Ghatak et al, IEE J. Quant. Electroni. 29 340 (1993)

    Article  ADS  Google Scholar 

  6. W Jing, M Yutao, T Lilin and L Zhijian Appl. Phys. Lett. 79 1831 (2001)

    Article  Google Scholar 

  7. A K Ghatak, I C Goyal, R Jindal and Y P Varshni Can. J. Phys. 76 351 (1998)

    Article  ADS  Google Scholar 

  8. A Sinha and R Roychoudry Int. J. Quant. Chem. 73 497 (1999)

    Article  Google Scholar 

  9. I C Goyal, R L Gallawa and A K Ghatak Opt. Lett. 16 30 (1991)

    Article  ADS  Google Scholar 

  10. I C Goyal, R Jindal and A K Ghatak J. Lightwave Technol. 15 2179 (1997)

    Article  ADS  Google Scholar 

  11. I C Goyal Modified Airy Function Solutions to Optical Waveguide Problems 1 155 2002

    Google Scholar 

  12. C-M Kim, Y-M Kim and W-K Kim IEEE J. Selected Topics in Quantum Electronics 8 (2002)

  13. María L Calvo and Vasudevan Lakshminarayanan Optical Waveguides: From Theory to Applied Technologies (USA: CRC Press) (2007)

    Google Scholar 

  14. I C Goyal, R L Gallawa and A K Ghatak J. Lightwave Technol. 11 (1993)

  15. L D Landau and E M Lifshitz Quantum Mechanics, Non-relativistic Theory (2nd edn), (Pergamon) (1965)

  16. M L Boas Mathematical methods in the Physical Sciences, (3rd edn), (NY: Wiley) (2006)

    MATH  Google Scholar 

  17. R L Liboff Introductory Quantum Mechanics (2nd edn), (NY: Addison Wesley) (1992)

    Google Scholar 

  18. A K Ghatak and S Lokhanathan Quantum mechanics: Theory and Applications, (New Delhi: Macmillan) (1984)

    Google Scholar 

  19. M Abramowitz and I A Stegun Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, US Dep. of Commerce, National Bureau of Standards, Washington DC, Applied Mathematical Series, (1970)

    Google Scholar 

  20. U Ascher and L Petzold SIAM J. Numer. Anal. 28 1097 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  21. H Shen and H J Silverstone Int. J. Quantum Chem. 99 336 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Science Faculty, Department of Physics Bornova, Ege University, Izmir, 35100, Turkey

    Murat Gerçeklioǧlu

  2. Faculty of Arts and Science, Department of Physics, Adnan Menderes University, Aytepe Mevkii, 09100, Aydin, Turkey

    Coşkun Deniz

Authors
  1. Coşkun Deniz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Murat Gerçeklioǧlu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Coşkun Deniz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deniz, C., Gerçeklioǧlu, M. An analysis of the exactly solvable linear differential equations by the Modified Airy Function (MAF) method. Indian J Phys 85, 339–357 (2011). https://doi.org/10.1007/s12648-011-0010-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-011-0010-1

Keywords

Search

Navigation