Abstract
The helium atom confined by a spherical parabolic potential well isstudied employing the adiabatic hyperspherical approach method. Total energiesof the ground and three low-excited states are obtained as a function of theconfined potential radii. We find that the energies of a spherical parabolicpotential well are in good agreement with those of an impenetrable sphericalbox for the larger confined potential radius. We find also that theconfinement may cause accidental degeneracies between levels with differentlow-excited states and the inversion of the energy values. The results forthe three-dimensional spherical potential well and the two-dimensionaldisc-like potential well are compared with each other. We find that theenergy difference between states in a two-dimensional parabolic potential isalso obviously larger than the corresponding levels for a sphericalparabolic potential.
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