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1 Complex Numbers in Quantum Mechanics
1 Complex Numbers in Quantum Mechanics

... of a coin toss is random, if we were willing to undertake the enormous task of solving the equations of motion taking account of all possible forces and carefully specifying the initial conditions, the outcome of a coin toss is predictable. In the same way, so-called hidden variable theories of quan ...
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... deviation equal to 20% of the mean value, thus representing a possible outcome of an experiment (Case 1). The shape of the distribution is usually unknown, but in this case we assume a priori a realistic shape, according to the bubble size measurement experiments of (Laakkonen et al 2006). Figure  1 ...
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The Property of Gases – Kinetic Molecular Theory

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Identical particles

Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to elementary particles such as electrons, composite subatomic particles such as atomic nuclei, as well as atoms and molecules. Quasiparticles also behave in this way. Although all known indistinguishable particles are ""tiny"", there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability; see particle statistics #Quantum statistics for detailed explication.There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which do not share quantum states due to the Pauli exclusion principle. Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei.The fact that particles can be identical has important consequences in statistical mechanics. Calculations in statistical mechanics rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behavior from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.
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