Magneto-optical absorption by electrons in the presence of parabolic confinement potentials

We study theoretically the absorption of long-wavelength perturbation by a many-electron system with externally imposed parabolic confinement potentials and a uniform magnetic field. It is shown that the absorption lines are at exactly the same frequencies as if there were only one electron. The general formulas for the frequencies and line-intensity ratios are found, and explicit analytical expressions are shown in some examples.