The carrier multiplication (CM) in spherical semiconductor quantum dots (QDs) as a re- sult of single photon absorption is studied. Semiconductors with simple parabolic electron- hole bands were considered when the band-to-band electron photon quantum transitions lead to creation of electron-hole (e-h) pairs with the same quantum numbers l, n, m of the envelope functions for electron and hole. In the frame of the perturbation theory the electron-radiation interband interaction with resonant and antiresonant terms as well as the electron-electron Coulomb interaction representing the long-range dipole-dipole interaction was engaged. A mechanism of the CM process similar with the packet balls in the billiards game is proposed. An alternative mechanism related with the quantum fluctuation in the electron- photon system leading to the simultaneous creation from the vacuum of one e-h pair and of a secondary photon is discussed. When their creation energies are supplied by the energy of the incident photon the CM process is accompanied by the Raman scattered photon. The creation of two and three e-h pairs in both variants is described. In both cases the first matrix elements between the initial state i and the first intermediary state 1 u are calculated on the base of resonant interband electron-radiation interaction. In the billiards packet ball mechanism the next matrix elements of the perturbation theory are calculated on the base of Coulomb interaction. When the quantum fluctuations are taken into account one of the next matrix elements is calculated on the base of the antiresonant part of the electron-radiation interaction. In the first case the CM process is characterized by a lorentzian-type absorption peak, whereas the CM accompanied by the Raman scattered photon is characterized by a smooth absorption plateau. This difference can explain the existence of the threshold on the frequency dependences of the CM quantum efficiency, in the spectral regions corresponding to creation of two or three e-h pairs in different QDs.