Description

About The Book

This book presents general formulas for various physical quantities in the hydrogenic system, such as average values of r raised to various integer powers represented by k, the most probable value of an electron for any given set of quantum numbers, the probability of finding an electron within any specified intervals, and so forth. The general formulas are extended to include different degrees, orders, and arguments (independent variables) of the associated Laguerre polynomials, facilitating the consideration of various scenarios. Additionally, the general formulas are developed for the product of multiple associated Laguerre polynomials, revealing that the final outcome can be represented in terms of Lauricella’s hypergeometric function.

These formulas possess a wide range of applications. Besides the previously noted uses, they have also been utilized to calculate the normalization constant for the radial eigenfunctions of the hydrogenic system in both spherical and parabolic coordinate systems. Additionally, we have employed these formulas to determine the normalization constant of the radial eigenfunctions related to the three-dimensional isotropic oscillator. These formulas entirely eliminate the dependence on the recursion relations.

Finally, I wish to highlight that two separate methods have been established for calculating the average values of r, whose exponent can vary among different integer values, and it has been shown that the application of the second method greatly simplifies the computation of these average values for lower negative integer values of k.

About The Author

The author has obtained a doctorate in lattice quantum chromodynamics (LQCD). His main areas of interest include particle physics, quantum chromodynamics, mathematical physics, and quantum mechanics. Currently, his research is centered on classical polynomials, hypergeometric functions, and differential equations.