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The term "particle" in this context refers to gaseous particles only (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium. [1] The energies of such particles follow what is known as Maxwell–Boltzmann statistics , and the statistical distribution of speeds is derived by equating particle ...
The general form of wavefunction for a system of particles, each with position r i and z-component of spin s z i. Sums are over the discrete variable s z , integrals over continuous positions r . For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is ...
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry.
Instantons are used in nonperturbative calculations of tunneling rates. Instantons have properties similar to particles, specific examples include: Calorons, finite temperature generalization of instantons. Merons, a field configuration which is a non-self-dual solution of the Yang–Mills field equation. The instanton is believed to be ...
Equilibrium thermal distributions for particles with integer spin (bosons), half integer spin (fermions), and classical (spinless) particles. Average occupancy is shown versus energy relative to the system chemical potential , where is the system temperature, and is the Boltzmann constant.
The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that ...
A solution describes a homogeneous mixture where the dispersed particles will not settle if the solution is left undisturbed for a prolonged period of time. A colloid is a heterogeneous mixture where the dispersed particles have at least in one direction a dimension roughly between 1 nm and 1 μm or that in a system discontinuities are found at ...
Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. Systems of many identical fermions are described by Fermi–Dirac statistics. Parastatistics are mathematically possible, but no examples exist in ...