Quantum Square Wells with Capacitive Walls: A Toy Model for Quantum Capacitors - Arifin Achmad (Jurnal Fisika dan Aplikasinya, 2025)
This research aims to determine the energy quantization in a one-dimensional infinite square well modified by capacitive walls. The electric field inside the wall produces a linear potential. The solution to the Schrdinger equation is the Airy function for an infinite square well. Furthermore, the Wentzel-KramersBrillouin (WKB) approach is applied to finite wells, and the energy quantization for both cases based on this modified potential has been derived. In this paper, we also examine the quantum capacitance of the system, which is determined from the density of states and depends on dimensionality. The result of this work is a toy model that does not yet provide a complete complex picture of the quantum capacitance model. However, this model shows similarities in terms of energy dispersion relations and quantum capacitance with several types of graphene systems