Studies on Shell Confined Atoms

This book presents a comprehensive exploration of the quantum mechanical behavior of atoms influenced by spatial confinement and screened Coulomb potentials-two pivotal factors in modern quantum theory and nanoscience. Spatial confinement introduces size-dependent quantum effects that fundamentally alter atomic properties such as ionization energies and polarizability, offering deep insights into systems at the nanoscale and under extreme pressures.In parallel, screened Coulomb interactions-modeled through potentials like the Hulthén, Yukawa, and exponential cosine screened Coulomb forms-capture essential short- and medium-range effects, highly relevant to plasmas, semiconductors, and condensed matter physics.Through analytical approximations and computational techniques, this work investigates the energy spectra and wavefunctions of hydrogen-like systems under both confinement and screening. Variational methods are employed to probe confined eigenstates, while numerical models are used to analyze the impact of potential screening on atomic behavior.Combining theoretical rigor with practical relevance, this book offers valuable perspectives for researchers in quantum mechanics.