A Comparative Analysis of Photon and Electron Wave Functions in Spherically Symmetric Potentials

А. А. Горват, В. Ю. Лазур, Олександр Костянтинович Рейтій

The relativistic version of WKB-method, allowing us to find the wave functions of a Dirac electron for spherically symmetric potentials in the classically allowed regions and in the forbidden region is developed. Using obtained wave functions, we compute the probability of Stark ionization of H-like ion in constant homogeneous electric field. Comparing of obtained results with the analogous data of non- relativistic approximation is carried out.

Avoy Jana

This paper presents a detailed analysis of the radial uncertainty product for quantum systems with spherically symmetric potentials. Using the principles of quantum mechanics, the study derives the radial uncertainty relation analogous to the Cartesian form and investigates its implications for three key spherically symmetric potentials: the Hydrogen atom, the infinite spherical potential well, and the spherical harmonic oscillator, all within the non-relativistic regime. Employing the Schrodinger equation in spherical coordinates, the paper rigorously evaluates the normalized radial wave functions, expectation values, and uncertainties associated with both position and momentum. Analytical derivations and numerical computations highlight the dependence of the uncertainty product on quantum numbers and system-specific parameters.

Jagdish Chandra, R. P. Gairola, B. D. Indu

The interpretation as well as derivation of the multi‐dimensional wave functions for spherically symmetric potentials is an uphill task in quantum mechanics. The wave functions for spherical harmonics are obtained in the context of hydrogen‐like atoms using the theory of Green's functions. The process of obtaining the Green's functions is new and is being reported for the first time. The process elucidates all the relevant features whatsoever required by the system. One of the salient features of the technique used is that it reduces all the hierarchies and higher‐order Green's functions to Green's functions of the lowest order.