LEVINSON THEOREM IN SEMICONDUCTOR QUANTUM DOTS

The Levinson's theorem in a semiconductor quantum dot is analysed. If the well and barrier effective masses differ, the zero-energy wavefunction phaseshift is shown to be eta(0) = piM(b) (M(b) being the number of bound states) for even values of azimuthal quantum number l, and pi(M(b) + 1) for odd l. For constant effective mass, however, eta(0) = piM(b) regardless of the parity of l. Furthermore, while eta --> 0 in the large-energy limit for the constant effective mass, the essentially different behaviour of eta takes place if the effective mass is non-uniform.