@inbook{69ff37a9fb8d430098e7cfcb5bbfe1f3,

title = "An Introduction to Special Functions with Some Applications to Quantum Mechanics",

abstract = "A short review on special functions and solution of the Coulomb problems in quantum mechanics is given. Multiparameter wave functions of linear harmonic oscillator, which cannot be obtained by the standard separation of variables, are discussed. Expectation values in relativistic Coulomb problems are studied by computer algebra methods.",

keywords = "Bessel functions, Chebyshev polynomials of a discrete variable, Dirac equation, Generalized hypergeometric series, Hahn polynomials, Laguerre polynomials, Nonrelativistic and relativistic Coulomb problems, Schr{\"o}dinger equation, Spherical harmonics",

author = "Suslov, {Sergei K.} and Vega-Guzm{\'a}n, {Jos{\'e} M.} and Kamal Barley",

note = "Funding Information: Acknowledgements We are very grateful to the organizers of the AIMS-Volkswagen Stiftung Workshop on Introduction to Orthogonal Polynomials and Applications held in Douala, Cameroon, in October 2018, without their help this publication would be impossible. Sincere thanks to our coauthors Christoph Koutschan, Sergey Kryuchkov, Raquel M. L{\'o}pez, Peter Paule and Erwin Suazo; some of our joint results were included in this chapter. We are very grateful to the referee for an outstanding job, her/his numerous comments helped us to improve the manuscript. Special thanks are directed to Jeremy Alm, Valentin Andreev, Al Boggess and Michael Laidacker for support and continuous encouragement. This work was partially supported by the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health (NIH; Grant # K12GM102778) and by the Lamar University Research Enhancement Grant (REG # 420266). Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

doi = "10.1007/978-3-030-36744-2_21",

language = "English (US)",

series = "Tutorials, Schools, and Workshops in the Mathematical Sciences",

publisher = "Birkhauser",

pages = "517--628",

booktitle = "Tutorials, Schools, and Workshops in the Mathematical Sciences",

}