The major themes of quantum mechanics are the physical interpretations of interactions in bound systems and particle scatterings. Stability of atoms and molecules is necessary in order that materials in nature could have any given determined physical and chemical properties, according to which these materials are distinguished and identified. Standard scattering theory has originally been introduced in nuclear physics, where the interactions are of short range, so that in the asymptotic region, the aggregates can be considered as being fully free. The required behaviours of the total scattering state are determined by the very nature of the interactions between the widely separated aggregates in the asymptotic region of scattering. In the old literature a terminological difference has sometimes been made between the notions of scattering and collision.
The major themes of quantum mechanics are the physical interpretations of interactions in bound systems and particle scatterings. Stability of atoms and molecules is necessary in order that materials in nature could have any given determined physical and chemical properties, according to which these materials are distinguished and identified. Standard scattering theory has originally been introduced in nuclear physics, where the interactions are of short range, so that in the asymptotic region, the aggregates can be considered as being fully free. The required behaviours of the total scattering state are determined by the very nature of the interactions between the widely separated aggregates in the asymptotic region of scattering. In the old literature a terminological difference has sometimes been made between the notions of scattering and collision.
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
Heisenberg offered an interpretation of the quantum state which made use of a quantitative version of an earlier notion, , of Aristotle by both referring to it using its Latin name,potentia, and identifying its qualitative aspect with . The relationship between this use and Aristotle's notion was not made by Heisenberg in full detail, beyond noting their common character: that of signifying the system's objective capacity to be found later to possess a property in actuality. For such actualization, Heisenberg requiredmeasurementto have taken place, an interaction with external systems that disrupts the otherwise independent, natural evolution of the quantum system. The notion of state actualization was later taken up by others, including Shimony, in the search for a law-like measurement process. Yet, the relation of quantum potentiality to Aristotle's original notion has been viewed as mainly terminological, even by those who used it thus. Here, I reconsider the relation of Heisenberg's notion to Aristotle's and show that it can be explicated in greater specificity than Heisenberg did. This is accomplished through the careful consideration of the role of potentia in physical causation and explanation, and done in order to provide a fuller understanding of this aspect of Heisenberg's approach to quantum mechanics. Most importantly, it is pointed out that Heisenberg's requirement of an external intervention during measurement that disrupts the otherwise independent, natural evolution of the quantum system is in accord with Aristotle's characterization of spontaneous causation. Thus, the need for a teleological understanding of the actualization of potentia, an often assumed requirement that has left this fundamental notion neglected, is seen to be spurious. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.
This chapter presents a descriptive introduction to the field of collision phenomena from the theoretical point of view, with the primary purpose of enumerating the fundamental themes of research as well as the relevant basic physical aspects. In the nonstationary treatment, collision is understood as a physical phenomenon which essentially develops in several time stages. Collisions between elementary particles are beyond the primary scope of the present work, because they would require relativistic quantum mechanics, considering, e.g., a target as an elementary particle, built from mesons, quarks, etc. Asymptotic convergence of scattering states is the most essential characteristic of the collision problem. This sole characteristic makes the collision phenomenon substantially different from the problem of finding bound states of the examined physical system for certain given interactions among the constituents.
Quantum mechanics has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. In this book, the author's emphasis is on helping students comprehend the significance of the underlying principles and understand the ways the new concepts were introduced. Including many worked examples and problems, this book will be an invaluable resource for students in physics, chemistry and electrical engineering needing a clear and rigorous introduction to quantum mechanics.
Conventional time‐independent scattering theories seem inadequate for dealing with collisions of ultracold atoms in the temperature range below a millikelvin, as the duration of such collisions is much longer than the radiative lifetimes of the electronically‐excited states involved. Neither is the total collision energy conserved following radiative decay, nor can one use energy eigenstates of the free atoms as stationary in asymptotes. A full treatment of radiatively‐damped collisions would require the solution of the Liouville‐Von Neumann (LVM) equations for the density matrix, with radiative decay introduced as a position‐dependent relaxation supermatrix (in the Markovian limit). However, the immense complexity of the problem, compounded by the lack of clearly defineable boundary conditions, can be largely avoided by exploiting the fact that the standard (damping‐free) problem can be solved for all collision energies. Using the stationary collision states (together with the bound states) as a basis, the LVM equations can be converted into a problem of ‘random walk among energy shells with traps’ involving radiative decay only. It follows that one can still use conventional scattering theory to define collision cross sections. However, instead of considering their values at a given energy, one must average them over a wide range of energies, the distribution of which is determined by the random‐walk problem. The radiative redistribution of energies affects the thermodynamic properties of cold‐atom traps, and may cause variations in the stability of systems based on different members of a fine‐structure multiplet.