Hydrogenic System and General Formulas for the Various Physical Quantities” by Devdatta M. Mankame is an important contribution to the field of quantum mechanics and mathematical physics. This book delves into the hydrogenic system with a focus on providing general formulas that address a wide array of physical quantities, offering researchers, students, and academicians a powerful resource for both theoretical and applied studies.
The book carefully develops general formulas for average values of r raised to various integer powers, the most probable value of an electron for a given set of quantum numbers, and probabilities of locating an electron within specific intervals. These formulations not only bring clarity but also create new possibilities for simplifying and extending complex calculations. By extending these general formulas to include different degrees, orders, and arguments of associated Laguerre polynomials, the author expands the applicability of the hydrogenic system to a broad range of scenarios.
A distinctive contribution of this work is the exploration of general formulas for the product of multiple associated Laguerre polynomials, with outcomes elegantly expressed in terms of Lauricella’s hypergeometric function. This approach provides a new perspective on classical polynomials and their role in quantum systems. The book also demonstrates the practical applications of these formulas by employing them to calculate normalization constants of radial eigenfunctions in spherical and parabolic coordinate systems, as well as for the three-dimensional isotropic oscillator. One of the key merits of these methods is that they completely eliminate reliance on recursion relations, thereby simplifying many traditionally cumbersome calculations.
Particularly noteworthy is the establishment of two separate methods for calculating average values of r for varying integer exponents. The author highlights that the second method offers remarkable simplification, especially for lower negative integer values of k, making it a highly valuable tool for researchers handling intricate quantum mechanical problems.
The author, Devdatta M. Mankame, brings a wealth of expertise to this subject. Having obtained his doctorate in lattice quantum chromodynamics (LQCD), his research interests span across particle physics, quantum chromodynamics, mathematical physics, and quantum mechanics. His current focus lies in the study of classical polynomials, hypergeometric functions, and differential equations, and this book is a reflection of his deep engagement with these areas.
“Hydrogenic System and General Formulas for the Various Physical Quantities” is not just a collection of advanced mathematical derivations, but also a practical guide that simplifies complex quantum mechanical computations. For scholars, physicists, and students aiming to deepen their understanding of hydrogenic systems and related mathematical frameworks, this book serves as both a reference and a pathway to further exploration. It is a significant addition to the growing body of literature in mathematical physics and will be of great benefit to those working at the intersection of mathematics and quantum theory.