The Schrödinger equation with a Gaussian potential to model a confined system as a quantum dot or a fullerene is solved using the Analytic Continuation Method. The use of the Rodrigues formula allows us to obtain in an easy way the coefficients of the power series expansion of the Gaussian potential in terms of the Hermite polynomials. Recurrence formulas have been obtained for the series of the states of a electron confined by that potential. This method is simpler and computationally more efficient than others employed to model quantum dots using Gaussian potentials.

In this work we studied the problem of the stability of confined atoms when they are released from confinement. We analyzed the confined Hydrogen atom inside a cage modelled by a square-well potential, in particular the effects of size on the energy and the electronic structure of the confined atom, by considering different internal radii of the confining cage. Starting from the confined wave function, we clarified the effect on the probability transition between different confined states, and characterized the stability of the atom when released from in term of both, the ionization probability and the transition probability to a bound state of the free atom. The values of the different atomic properties calculated present oscillations when they are studied as a function of the size of the confining cage. This behavior can be explained in terms of the shell structure of the atom.

In this study, we address the problem of the C$_{60}$ endohedrally confined Hydrogen molecule through a Configuration-Interaction approach to the electronic dynamics. Modeling the confinement by means of a combination...

The ground state energy of a helium atom inside a spherical multilayer quantum dot as a function of the atomic impurity location inside the quantum dot has been calculated. The multilayer quantum dot is modeled by a core/shell/well/shell structure using a parabolic confinement. The Configuration Interaction method and the Diffusion Monte Carlo have been used to solve the Schrödinger equation. Results obtained showed that the lowest energy configuration depends on the size of the different layers of the quantum dot and agreement between Configuration Interaction and Diffusion Monte Carlo results indicates that the Configuration Interaction approach used here would be suitable to compute excited states of this system. Graphical abstract