Tailoring masses to artificial molecules based on the shape of their wavefunctions

In this short paper, we examine artificial molecules composed of coupled artificial atoms such as quantum dots. Similar to artificial atoms, which have position-dependent effective masses for electrons, artificial molecules exhibit this characteristic while comprising more than one artificial atom. While in the literature, such artificial molecules are focused on the kinetic term of the electrons in such a setup, we consider the full description that includes the kinetic and potential terms that involve the nuclei. The proposed artificial molecules consist of nuclei and electrons coupled through Coulomb potentials and kinetic energy influenced by electronic position-dependent effective masses that also depend on the positions of the nuclei and the other electrons in the system. We demonstrate how the Schrödinger equation for such systems can be solved by assuming the entire shape of the molecular wavefunction, guided by a tailored non-parabolic energy-momentum relation for at least one electron within the molecular structure. Additionally, we show that instead of pre-specifying the entire form of the molecular wavefunction, we can consider the coupling between the electrons and nuclei to obtain the wavefunction of the system.