The hydrogen atom within spherical boxes with penetrable walls

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Abstract
We study a model for the hydrogen atom confined within spherical boxes with penetrable walls. The potential consists of the Coulomb potential inside the box and a constant potential outside the box; the Schrödinger equation admits analytical solutions in both regions. The energy eigenvalues and eigenfunctions for the lowest states of the system are determined numerically for boxes of different sizes and penetrabilities. In addition, we also evaluate the hyperfine splitting, nuclear magnetic shielding, polarizability and pressure of the system and investigate the effect of the confinement on these atomic properties.