Introduction and review of quantum mechanics

Mark Linne

Luigi Barletti

The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of \nthe Wigner transform and eventually deduce the Wigner equation.

Kenichi Konishi, Giampiero Paffuti

Abstract Physical phenomena in the microscopic world are extraordinary and often appear even paradoxical from the viewpoint of our daily experiences. A closer look, however, shows that they possess a simple and elegant logic of their own. By way of introduction to this entire volume on quantum mechanics, let us discuss a few such features, taking the example of the electron. We then briefly review the historical development which led to the discovery of quantum mechanics.

Michael Gonzalez

Tarit K. Bose

Fernando Parisio, D. Felinto, Matheus Cândia Araña +2 more

Quantum biology explores the possibility that fundamental quantum phenomena—such as coherence, tunneling, and entanglement—play functional roles in living systems. While biological environments are warm, wet, and noisy, making them seemingly inhospitable to quantum effects, a growing body of theoretical and experimental work suggests that quantum mechanics may influence processes at the molecular and cellular scale. In this review, we provide a concise introduction to the essential concepts of quantum mechanics most relevant to biology through an exploration of the radical pair mechanism, theorized to play a role in avian navigation during the migratory season. We examine the radical pair mechanism step-by-step from activation to recombination, introducing the concepts from quantum mechanics necessary to start to understand the full workings of the mechanism. By balancing pedagogical clarity with critical evaluation, this review aims to provide both newcomers and specialists with an accessible entry point into quantum biology and to point toward the interdisciplinary challenges and opportunities that lie ahead.