Аннотация:Some analytical and numerical features of the one-electron atom in a spherical cavity with impenetrable walls problem, being a widely used simple model for the electronic structure of atoms in the bounded volume (e.g., trapped into the cavities formed by zeolites, fullerenes or situated inside the dot-like clusters), are discussed. The energy levels of the system are studied as functions of the radius of cavity, and some rigorous rules on the possibility of degeneration of energy levels corresponding to different angular momentum values, are formulated. The results obtained show that eigenstates with high angular momentum values are to be taken into account in the quantum-mechanical treatment of atoms and molecules in the bounded volume.
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