Exact solutions for shell-confined hydrogen-like atoms:polarizabilities and Shannon entropies

Brian Lancelot Burrows (1) , Maurice Cohen (2)

1 Faculty of Computing,Engineering and Technology
2 Department of Physical Chemistry

An idealized model to treat the effect of spherically confining the electron in a hydrogen -like atom is studied, where the potential is infinite in all space except for a spherical shell. The exact solution of the Schrodinger equation is obtained in terms of two independent solutions of the Kummer equations. It is found that in some cases it is necessary to use the standard KummerM function and a non-standard second solution. In other cases we may use the KummerU function and in a limiting case the two standard solutions of Bessel's equation. The effect of an imposed dipole field on the shell is treated using the first-order perturbation equation from which the polarizability can be calculated. In addition the exact wavefunction is used to calculate the Shannon entropies of both position and momentum and it is shown that these measures give insight into the form of the wavefunction.

Mots clés: Physical Sciences

Brian Lancelot Burrows, Maurice Cohen. Exact solutions for shell-confined hydrogen-like atoms:polarizabilities and Shannon entropies. Molecular Physics, 2008, 106 (02-04), pp.267-273. ⟨10.1080/00268970701787864⟩. ⟨hal-00513163⟩