One electron quantum dots with positive coulomb impurity under high pressure: tunable degeneracy, information-theoretic and response measures

Abstract A comprehensive investigation of one-electron quantum dots (OEQDs) in free and confined conditions is presented, with emphasis placed on degeneracy patterns, information-theoretic measures, and response properties. Highly accurate results connecting 1 s , 2 p , 2 s and 3 d states are obtained by employing the generalized pseudospectral method. The effects of the potential depth ( A ), cavity constant ( B ), and the confinement radius r c are systematically analyzed. Localization is found to be enhanced with increasing A , while delocalization is induced by B ; in the asymptotic limits B → 0 and B → ∞ , hydrogenic behavior is recovered. Three generalized scaling relations are derived, through which a unified framework connecting effective Hamiltonians is established. Accidental degeneracies among the 2 s –2 p , 3 p –3 d , and 3 s –3 d states are identified, and the validity of a virial-like theorem in OEQDs is confirmed. Localization–delocalization trends and similarities between degenerate states are characterized using Shannon entropy and relative Shannon entropy, and a relation connecting Shannon entropy, oscillator strengths, and orbital energies is proposed and validated. Polarizability calculations disclose the presence of tune-out points in both free and confined (OEQDs), characterized by vanishing dipole response. It is thereby demonstrated that the electronic structure and spectroscopic features of OEQDs can be precisely controlled through appropriate variation of A , B , and r c , with implications for confined atomic systems and prospective qubit architectures.