Particle density distribution in a pyramid-shaped quantum well

This paper is focused on analytical solution of the quantum–mechanical problem describing a particle confined into a pyramid-shaped quantum well. This type of micro- and nano-scale objects can be formed on the surface of semiconductor material as texturing elements for solar cells, Bragg reflectors, quantum dot lasers, etc. The problem was treated using specular reflections of plain wave functions of the particle from the sides of the pyramid. Defining a closed group of symmetry transformations for the system, we solve Schrödinger equation in the Cartesian coordinates. This wave function was used to calculate three-dimensional distributions of particle probability density within a square-based pyramid. Analysis of excited states energy reported in publications shown good correlation between our theoretical calculations and experimental data.