Energy spectra of an exciton in a Gaussian potential and magnetic field

We explore an exciton quantum dot in a Gaussian confining potential and an external magnetic field. By means of numerical matrix diagonalization within the effective-mass approximation we obtain the energy spectrum and show that the property of low-lying states of the quantum dot is rather sensitive to the magnetic field and the strength of the confinement potential as well. The dependence of energy spectrum of the low-lying states on the magnetic field and the size of the confining potential is analyzed explicitly