Quantum-size states of the deformed nanosphere

The effect of shape deformation of a spherical nano-object on quantum states of a particle in it has been analyzed theoretically. For this purpose, a functional method of surface shape perturbation theory has been proposed. The method allows us to determine the effect of a wide range of deviations of a limited three-dimensional volume (nano-object) from the initial shape on the quantum characteristics of a charge localized inside the nano-object. An analysis has demonstrated that the probability density for a particle in quantum-size states is more sensitive to surface shape perturbations than the energy spectrum and the density of quantum states. Even small shape perturbations lead to a smearing of the probability density for the location of a particle inside a nano-object and lift the degeneracy in the magnetic quantum number. A mixing of pure states corresponding to a sphere has been observed. The degree of mixing and the splitting of the energy levels increase with increasing quantum numbers $l$ and $m$.