The objective of this paper is to present a mathematical formalism that states a bridge between Physics and Psychology, concretely between analytical dynamics and personality theory in order to open new insights in this theory. In this formalism energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modelled by a stimulus-response model: an integro-differential equation. The bridge between Physics and Psychology is provided when the stimulus-response model can be formulated as a linear second order differential equation and, subsequently, reformulated as a Newtonian equation. This bridge is strengthened when the Newtonian equation is derived from a minimum action principle, obtaining the current Lagrangian and Hamiltonian functions. However, the Hamiltonian is a non-conserved energy. Then, some changes provide a conserved Hamiltonian function: the Ermakov-Lewis energy. This energy is presented, as well as the GFP dynamical response that can be derived from it. An application case is presented: an experimental design in which 28 individuals consumed 26.51 g of alcohol. This experiment provides an ordinal scale for the Ermakov-Lewis energies that predicts the effect of a single dose of alcohol.

This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first order differential equations. They are referred as “abstract” because their dynamical variables can be of different interrelated nature, not necessarily corresponding to physics, such as populations, socioeconomic variables, behavioural variables, etc. A first order classical Hamiltonian in canonical moments can be derived for ADS by using Dirac’s dynamics for singular Hamiltonian systems. And also a corresponding first order Schrödinger equation (which involves the existence of a system Planck constant particular of each system) can be derived from this Hamiltonian. However, Bohm and Hiley’s reinterpretation of quantum mechanics produces no further information about the mathematical formulation of ADS. However, a second order classical Hamiltonian in canonical moments can be also derived for ADS, as well as a corresponding second order Schrödinger equation. In this case, Bohm and Hiley’s reinterpretation of quantum mechanics provides a quantum Hamiltonian that does provide the quantum formulation for ADS, which provides new quantum variables interrelated dynamically with the classical variables. An application case is presented: the one-dimensional autonomous system given by the logistic dynamics, where the differences between the classical and the quantum trajectories are highlighted.