Abstract
In the first two sections of this chapter we explain results from theory of functions of a complex variables and from theory of differential equations. These results will be needed for different applications in later chapters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bhalla R.S.: The Quantum Hamilton-Jacobi Formalism Approach to Energy Spectra of Potential Problems, Ph. D. Thesis submitted to University of Hyderabad, 1996
Bhalla, R.S., Kapoor, A.K., Panigrahi, P.K.: Quantum Hamilton-Jacobi formalism and bound state spectra. Am. J. Phys. 65, 1187 (1997)
Leacock, R.A., Padgett, J.: Hamilton-Jacobi Theory and the quantum action variable. Phys. Rev. Lett. 50, 3 (1983)
Leacock, R.A., Padgett, M.J.: Hamilton-Jacobi Action angle quantum mechanics. Phys. Rev. D 28, 2491 (1983)
Churchill Ruel Vance and Brown James: Complex Variables and Applications. McGraw-Hill Publishing Book Co., New York (2014)
Titchmarsh, E.C.: The Theory of Functions. Oxford University Press, United Kingdom (1964)
Ince, E.L.: Ordinary Differential Equations. Dover Publications, New York (1956)
Einar, Hille: Ordinary Differential Equations in Complex Domain. Wiley Interscience Publications, New York (1976)
Piaggio, H.T.H.: An Elementary Treatise on Differential Equations and Their Applications. B. Bell and Sons, London (1949)
Shabat, A., Kartashova, E.: Computable Integrability. arXiv:1103.2423v1
Reid, W.T.: Riccati Differential Equations. Academic Press, New York and London (1972)
Kapoor, A.K.: Complex Variables—Principles and Problem Sessions, World Scientific Publishing Co. Pte. Ltd., Singapore (2011); For errata, visit. https://0space.org/node/3488
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kapoor, A.K., Panigrahi, P.K., Ranjani, S.S. (2022). Mathematical Preliminaries. In: Quantum Hamilton-Jacobi Formalism. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-10624-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-10624-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-10623-1
Online ISBN: 978-3-031-10624-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)