Confined orbitals in fullerenes and quantum dots calculated by analytic continuation method

Abstract

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.

Topological effects of a global monopole on a spherical quantum dot

“…In [42], the attractive short-hand potential proposed was a Gaussian confining potential. Other interesting studies that have explored the Gaussian confining potential are given in [44][45][46][47][48]. From the perspective of describing a quantum dot through an attractive short-range potential, Ciurla et al [43] proposed a model called the power-exponential potential [43].…”

“…where p ≥ 1, V 0 > 0 is the depth of the confinement potential, r is the radial coordinate and r 0 is the range of the confinement potential. Quantum dots described by the power-exponential potential (1.1) have been explored in [42][43][44][45][46][47][48]. For p = 2, equation (1.1) describes the attractive Gaussian potential [42,[46][47][48].…”

Effects of size on the spectrum and stability of a confined on-center Hydrogen atom

“…Different models of confinement have been proposed to study the properties of confined atoms and molecules, most of which use a potential barrier to model the confinement. Among the models proposed are the infinite [55][56][57][58] or finite [59][60][61] spherical barrier, the harmonic potential [51], a parabolic confinement [62], the gaussian potential [63][64][65][66][67], the square-well potential [32,[68][69][70][71], a combination of Woods-Saxon potentials [60,72,73], and Lorenztian functions [74]. In the case of fullerenes, the use of the square-well potential or a combination of Woods-Saxon potentials provides suitable results in agreement with experiment [75].…”

Spherical quantum dot described by a scalar exponential potential under the influence of a linear scalar potential and a global monopole

“…By working with the spherical symmetry, then, r corresponds to the radial coordinate. The potential energy (1) describes an attractive short-range potential [1][2][3][4], where for p = 2 we have the attractive Gaussian potential [1,[5][6][7]. Moreover, we have a rectangular potential for p → ∞.…”