ABSTRACT

In this paper, the Schr?dinger equation is solved by Modified separation of variables (MSV)
method suggested by Pishkoo and Darus. Using this method, Meijer’s *G*-function solutions are derived in cylindrical
coordinate system for quantum particle in cylindrical can. All
elementary functions and most of the special functions which are the solution
of extensive problems in physics and engineering are special cases of Meijer’s *G*-functions.

Cite this paper

A. Pishkoo and M. Darus, "*G*-Function Solutions for Schrödinger Equation in Cylindrical Coordinates System," *Applied Mathematics*, Vol. 5 No. 3, 2014, pp. 342-346. doi: 10.4236/am.2014.53035.

A. Pishkoo and M. Darus, "

References

[1] V. Kiryakova, “Generalized Fractional Calculus and Applications, Vol. 301,” Chapman & Hall/CRC, London, 1994.

[2] L. Andrews, “Special Functions for Engineers and Applied Mathematicians,” Macmillan, 1985.

[3] Y. Luck, “The Special Functions and Their Approximations, Complex Variables,” Academic Press, New York, 1969.

[4] R. Askey, “Meijer G-Function,” Cambridge University Press, Cambridge, 2010.

[5] A. Klimyik, “Meijer G-Function,” Springer, Berlin, 2001.

[6] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, “Higher Transcendental Functions,” McGraw-Hill, New York, 1953.

[7] A. Prudnikov, I. Brychkov and O. Marichev, “Integrals and Series: Some More Special Functions,” Gordon & Breach, Philadelphia, 1992.

[8] A. Kilbas, H. Srivastava and J. Trujillo, “Theory and Applications of Fractional Differential Equations,” Elsevier, Amsterdam, 2006.

[9] A. Pishkoo and M. Darus, “Meijer’s G-Functions (MGFs) in Microand Nanostructures,” Journal of Computational and Theoretical Nanoscience, Vol. 10, No. 10, 2013, pp. 2478-2483.

http://dx.doi.org/10.1166/jctn.2013.3234

[10] A. Pishkoo and M. Darus, “Some Applications of Meijer G-Functions as Solutions of Differential Equations in Physical Models,” Journal of Mathematical Physics, Analysis, Geometry, Vol. 3, No. 9, 2013, pp. 379-391.

[11] A. Pishkoo and M. Darus, “Meijer’s G-Functions as the Solution of Schrodinger Equation,” Proceeding of the 43rd Iranian Mathematics Conference, University of Tabriz, Tabriz, 27-30 August 2012.

[12] A. Pishkoo and M. Darus, “G-Function Solutions for Diffusion and Laplace’s Equations,” Journal of Advances in Mathematics, Vol. 4, No. 1, 2013, pp. 359-365.

[13] S. Hassani, “Mathematical Physics: A Modern Introduction to Its Foundations,” Springer, New York, 1998.

[14] A. Pishkoo and M. Darus, “Fractional Differintegral Transformations of Univalent Meijer’s G-Functions,” Journal of Inequalities and Applications, Vol. 2012, 2012, p. 36. http://dx.doi.org/10.1186/1029-242X-2012-36

[1] V. Kiryakova, “Generalized Fractional Calculus and Applications, Vol. 301,” Chapman & Hall/CRC, London, 1994.

[2] L. Andrews, “Special Functions for Engineers and Applied Mathematicians,” Macmillan, 1985.

[3] Y. Luck, “The Special Functions and Their Approximations, Complex Variables,” Academic Press, New York, 1969.

[4] R. Askey, “Meijer G-Function,” Cambridge University Press, Cambridge, 2010.

[5] A. Klimyik, “Meijer G-Function,” Springer, Berlin, 2001.

[6] A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, “Higher Transcendental Functions,” McGraw-Hill, New York, 1953.

[7] A. Prudnikov, I. Brychkov and O. Marichev, “Integrals and Series: Some More Special Functions,” Gordon & Breach, Philadelphia, 1992.

[8] A. Kilbas, H. Srivastava and J. Trujillo, “Theory and Applications of Fractional Differential Equations,” Elsevier, Amsterdam, 2006.

[9] A. Pishkoo and M. Darus, “Meijer’s G-Functions (MGFs) in Microand Nanostructures,” Journal of Computational and Theoretical Nanoscience, Vol. 10, No. 10, 2013, pp. 2478-2483.

http://dx.doi.org/10.1166/jctn.2013.3234

[10] A. Pishkoo and M. Darus, “Some Applications of Meijer G-Functions as Solutions of Differential Equations in Physical Models,” Journal of Mathematical Physics, Analysis, Geometry, Vol. 3, No. 9, 2013, pp. 379-391.

[11] A. Pishkoo and M. Darus, “Meijer’s G-Functions as the Solution of Schrodinger Equation,” Proceeding of the 43rd Iranian Mathematics Conference, University of Tabriz, Tabriz, 27-30 August 2012.

[12] A. Pishkoo and M. Darus, “G-Function Solutions for Diffusion and Laplace’s Equations,” Journal of Advances in Mathematics, Vol. 4, No. 1, 2013, pp. 359-365.

[13] S. Hassani, “Mathematical Physics: A Modern Introduction to Its Foundations,” Springer, New York, 1998.

[14] A. Pishkoo and M. Darus, “Fractional Differintegral Transformations of Univalent Meijer’s G-Functions,” Journal of Inequalities and Applications, Vol. 2012, 2012, p. 36. http://dx.doi.org/10.1186/1029-242X-2012-36