Sudden change in the equilibrium position and oscillator quantum transitions in the tomographic representation

Abstract

The transition probabilities during instantaneous change in the quantum oscillator equilibrium position are studied in the tomographic representation. A comparison with the known Franck-Condon factors obtained by calculating the wave function overlap integrals is performed. Explicit expressions for symplectic and optical tomograms are derived, as well as the generating function for overlap integrals of symplectic tomograms defining the transition probabilities in the oscillator, caused by the driving force.