Introduction to quantum mechanicsQuantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain.
Maxwell–Boltzmann distributionIn physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment.
Squeezed coherent stateIn physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position and momentum of a particle, and the (dimension-less) electric field in the amplitude (phase 0) and in the mode (phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle: and , respectively.
H-theoremIn classical statistical mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity H (defined below) in a nearly-ideal gas of molecules. As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics.
Density matrixIn quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states.
Virtual particleA virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.
Particle numberIn thermodynamics, the particle number (symbol N) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential. Unlike most physical quantities, the particle number is a dimensionless quantity, specifically a countable quantity. It is an extensive property, as it is directly proportional to the size of the system under consideration and thus meaningful only for closed systems.
Fermi gasA Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi.
Thermal equilibriumTwo physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant. Systems in thermodynamic equilibrium are always in thermal equilibrium, but the converse is not always true.
Non-equilibrium thermodynamicsNon-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.
