The information-theoretic measure of confined hydrogen atom has been investigated extensively in the literature. However, most of them were focused on the ground state and accurate values of information entropies, such as Shannon entropy, for confined hydrogen are still not determined. In this work, we establish the benchmark results of the Shannon entropy for confined hydrogen atom in a spherical impenetrable sphere, in both position and momentum spaces. This is done by examining the bound state energies, the normalization of wave functions, and the scaling property with respect to isoelectronic hydrogenic ions. The angular and radial parts of Shannon entropy in two conjugate spaces are provided in detail for both free and confined hydrogen atom in ground and several excited states. The entropies in position space decrease logarithmically with decreasing the size of confinement, while those in momentum space increase logarithmically. The Shannon entropy sum, however, approaches to finite values when the confinement radius closes to zero. It is also found that the Shannon entropy sum shares same trend for states with similar density distributions. Variations of entropy for nodeless bound states are significantly distinct form those owning nodes when changing the confinement radius. K E Y W O R D S confined hydrogen atom, momentum space, radial entropy, Shannon entropy Int J Quantum Chem. 2017;117:e25375. https://doi.org/10.1002/qua.25375.

The critical screening parameters for one-electron systems screened by Hulthén, Debye–Hückel, and exponential cosine screened Coulomb potentials are calculated with an accuracy close to the precision of numerical arithmetic. The results for a H atom with an infinitely heavy nucleus are reported from the ground to high-lying excited states, and those for arbitrary two-body charged systems are derived from the Zm-scaling law. A thorough comparison of the critical screening parameters for the ground and the first p-wave excited states with previous predictions is made to demonstrate the accuracy of our calculations. The critical behaviors of system-bound and pseudo-continuum eigenenergies for s- and non-s-wave states are shown to follow the quadratic and linear laws, respectively. The variation of the corresponding wave functions is analyzed in detail. For systems with non-zero orbital angular momenta, the bound states convert into shape-type resonances when the screening parameter exceeds the critical value. The resonance energy shares the same linear law as the pseudo-continuum state, while the resonance width varies by an l-dependent power law. It is further shown that the different asymptotic behaviors of the resonance energy and width are consistent with the complex analog of the Hellmann–Feynman theorem.

The uncertainties inherent in the normalization of subgap photoconductivity spectra to the optical absorption spectra α(hv) in a-Si:H based films have been addressed. An analysis is presented which is based on optical transitions of constant dipole matrix element between parabolic distributions of extended states and exponential distributions of localized tail states. This analysis has been used to normalize the two sets of results accurately, as verified by photothermal deflection spectroscopy measurements, and is shown to be useful in the commonly encountered cases, in which the two spectra do not overlap over an extended region. Improved quantitative fits of α(hv), for photon energy from ∼1.5 to 2.4 eV, obtained on different a-Si:H based films indicate that the localized exponential band tail regions extend ∼60–70 meV above the optical gap.

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