Molar absorptivity and probability of transition

Abstract

The interaction between matter and light, or electromagnetic radiation, is essential for understanding the properties of materials. This interaction is often analyzed through absorption spectroscopy, based on the Lambert-Beer Law. Initially described by Pierre Bouguer, later formalized by Johann Lambert, and extended by August Beer, this law establishes a mathematical relationship between light absorption, the optical properties of the medium, and the concentration of absorbing species. According to this law, light intensity decreases logarithmically as it passes through an absorbing substance.

Quantum mechanics provides an important framework for describing electronic transitions between different energy states in atoms and molecules, utilizing time-dependent perturbation theory. This theory relates energy transitions to the transition moment, derived from the time-dependent Schrödinger equation, determining the probability of electronic transitions occurring.

Before the advent of quantum mechanics, Einstein introduced a classical interpretation of electronic transitions, presenting the coefficients of absorption and emission, both spontaneous and stimulated. These coefficients connect classical parameters, such as the absorption coefficient and molar absorptivity, to probabilistic concepts and the solutions of the time-dependent Schrödinger equation, bridging classical and quantum perspectives in the study of light absorption.