Seminarium Optyczne

Abstract. A model of living systems considered as coherent, time-dependentanharmonic oscillators is presented. It is based on the concept ofspace-like coherent states minimizing the time-energy uncertaintyrelation, adapted to the case of biological systems whose growth isdescribed by the Gompertz or West-Brown-Enquist functions. The coherentstates of biological growth evolve coherently in space being localizedalong the classical time trajectory; hence, the growth is predicted to becoherent in space. It is proven that the Gompertz function is a specialsolution of the space-like Horodecki-Feinberg equation for thetime-dependent Morse oscillator in the dissociation state. Its eigenvaluerepresents the momentum of biological growth, associated with a space-likecomponent whose properties resemble those attributed by vitalists to thelife momentum or vital impulse. The physical characteristics of the lifeenergy and momentum and their connection with the concept of zero-pointmomentum of vacuum are presented.