Optical “visualization” of Pythagorean triples and electrostatic multipoles in quantum dash

The problem of the features of the electron energy spectrum in a quantum parallelepiped has been considered. The family of triply degenerate energy levels has been found for the chosen model of the quantum parallelepiped. The optical transitions in this system has been investigated. It has been established that primitive Pythagorean triples are in the basis of every family of triply degenerate levels and this fact is directly reflected on the optical properties of the quantum dashes. In particular, due to the selection rules for the electronic transitions, it is possible to "visualize" Pythagorean triples theoretically. The dependence of absorption coefficient on the incident photon energy of quantum dash ensemble has been studied. The dipole, quadrupole moments and the electrostatic field created by the electron localized in a quantum dash have been investigated.