ENERGY LEVELS AND WAVE FUNCTIONS OF ELLIPSOIDAL NANOPARTICLE

Author: davit kereselidze
Keywords: Ellipsoidal nanoparticle, the perturbation theory, the direct method of Hamiltonian diagonalization
Annotation:

In this work, we’ll define the energy spectrum and appropriate wave functions of charged particle, which is trapped in ellipsoidal potential well with infinitely high walls. For this, we’ll use two points of view: the perturbation theory and the direct method of Hamiltonian diagonalization. When nanoparticle’s shape differs from spherical a little, we’ll determine together the first, the second and the third corrections of energies for charged particle and the first, the second corrections of wave functions. To help through the direct method of Hamiltonian diagonalization, we’ll write an algebraic equation, which solves analytically in the separate cases. After this, we’ll compare our results with the results of other authors and determine the region of application analytical formulas. At last, we’ll speak about optical properties of ellipsoidal nanoparticles. More concrete, we’ll see that space anisotropy determines the energies of ellipsoidal potential well from infrared including ultraviolet transitions. Also, it seems that it possible to regulate emission and absorption spectra of nanoparticles by shape and size variation.

Lecture files:

ელიფსოიდური ფორმის ნანონაწილაკის ენერგეტიკული დონეები და ტალღური ფუნქციები [ka]
ელიფსოიდური ფორმის ნანონაწილაკის ენერგეტიკული დონეები და ტალღური ფუნქციები [ka]