Optical properties of parabolic quantum wires in the presence of electron-electron interactions: An Euler-Lagrange variational application

In this work, we investigate the absorption coefficient and refractive index changes of a parabolic quantum well in the presence of electron-electron interactions. We use a nonlinear term in our Schrödinger equation to simulate the electron-electron interaction effect. We solve the resulting nonlinear Schrödinger equation through an Euler-Lagrange variational method. We study the effects of interaction strength and geometrical potential on energy levels, eigenfunctions, absorption coefficient and refractive index changes. We show that, Electron-electron interaction strength tries to delocalize the wavefunction while geometrical parabolic potential parameter tries to localize it. Thus, by means of these parameters we are able to control the electron confinement and wave function localization. In the literatures, it is usually stated that the electron-electron instructions can be neglected in optical properties investigations. But, when we increase the electron-electron interaction strength from 0 to 1 eV (from null to full electron-electron interaction), the absorption coefficient increases up to 20%, thus it cannot be neglected.