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Note that this "high temperature" approximation does not distinguish between fermions and bosons. The discrepancy in the partition functions of distinguishable and indistinguishable particles was known as far back as the 19th century, before the advent of quantum mechanics. It leads to a difficulty known as the Gibbs paradox.
The name boson was coined by Paul Dirac [3] [4] to commemorate the contribution of Satyendra Nath Bose, an Indian physicist. When Bose was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh), [5] [6] he and Albert Einstein developed the theory characterising such particles, now known as Bose–Einstein statistics and Bose–Einstein condensate.
Bosons are one of the two fundamental particles having integral spinclasses of particles, the other being fermions. Bosons are characterized by Bose–Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons. According to the Standard Model, the elementary bosons are:
A counterpart to Fermi–Dirac statistics is Bose–Einstein statistics, which applies to identical and indistinguishable particles with integer spin (0, 1, 2, etc.) called bosons. In classical physics, Maxwell–Boltzmann statistics is used to describe particles that are identical and treated as distinguishable. For both Bose–Einstein and ...
In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density of measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called normalization .
At low temperatures, bosons behave differently from fermions (which obey the Fermi–Dirac statistics) in a way that an unlimited number of them can "condense" into the same energy state. This apparently unusual property also gives rise to the special state of matter – the Bose–Einstein condensate .
i.e., on transposition of the arguments of any two particles the wavefunction should reproduce, apart from a prefactor (−1) 2S which is +1 for bosons, but (−1) for fermions. Electrons are fermions with S = 1/2; quanta of light are bosons with S = 1. Due to the form of anti-symmetrized wavefunction:
For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation. Exchange interaction effects were discovered independently by physicists Werner Heisenberg and Paul Dirac in 1926. [4 ...