- Research Article
- 10.1088/1402-4896/ae3f62
One electron quantum dots with positive coulomb impurity under high pressure: tunable degeneracy, information-theoretic and response measures
- Feb 10, 2026
- Physica Scripta
- Neetik Mukherjee
Abstract A comprehensive investigation of {\color{red}one-electron} quantum dots {\color{red}(OEQDs)} in free and confined conditions is 
presented, with emphasis placed on degeneracy patterns, information-theoretic measures, and response properties. Highly accurate 
results connecting $1s$, $2p$, $2s$ and $3d$ states are obtained by employing the generalized pseudospectral method. The effects of 
the potential {\color{red} 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 $B \to 0$ and $B \to \infty$, 
hydrogenic behavior is recovered. Three generalized scaling relations are derived, through which a unified framework connecting effective 
Hamiltonians is established. Accidental degeneracies among the $2s$–$2p$, $3p$–$3d$, and $3s$–$3d$ states are identified, and the validity of a virial-like theorem in {\color{red}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 {\color{red}(OEQDs)}, characterized by vanishing dipole response. It is thereby demonstrated that the electronic structure and spectroscopic features of {\color{red}OEQDs} can be precisely controlled through appropriate variation of $A$, $B$, and $r_{c}$, with implications for confined atomic systems and prospective qubit architectures. \\
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