New wavefunctions for the excited states of an axial impurity in a quantum wire

Spectral Parameters of Electron in a Multishell Semiconductor Cylindrical Nanotube with a Donor Impurity at Its Axis

“…The research of the binding energy of an electron with an impurity in cylindrical quantum wires or simple nanotubes faces the considerable mathematical difficulties associated with the fact that the spherical symmetry of the Coulomb interaction potential between the electron and the impurity and the nonspherical symmetry of the system have to be put in agreement with each other. Therefore, while studying the impurity-renormalized electron spectrum, the authors use the Ritz variational method in the overwhelming majority of works [10][11][12][13][14][15][16]. However, this method allows only the ground state of an electron to be described rather exactly and simply.…”

The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

“…[1-7].Box models of quantum confinement have shown to be appropriate to survey the effect of spatial limitation on the electronic properties of caged atoms and molecules to mimic high pressure conditions [2,[8][9][10][11][12][13][14][15] as well as to explain the behavior of donor states in semiconductor quantum dots (QD's). [16][17][18][19][20][21][22][23][24][25][26][27] In the latter case, the spectroscopic techniques used to characterize the optical properties of hydrogenic donor impurities embedded in semiconductor QD's pose the need of appropriate theoretical treatments to account for differences in the electronic level structure due to changes in the shape of the QD as well as in the enclosed impurity position. A good deal of theoretical work has been addressed to study the behavior of hydrogenic donor states in spherical QD's.…”