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According to Asher Peres [4] and David Kaiser, [5] the publication of the 1982 proof of the no-cloning theorem by Wootters and Zurek [2] and by Dieks [3] was prompted by a proposal of Nick Herbert [6] for a superluminal communication device using quantum entanglement, and Giancarlo Ghirardi [7] had proven the theorem 18 months prior to the published proof by Wootters and Zurek in his referee ...
In thermodynamics, the particle number (symbol N) of a thermodynamic system is the number of constituent particles in that system. [1] 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 ...
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The following is in bra–ket notation : The number operator acts on Fock space .
For example, distributing two particles in three sublevels will give population numbers of 110, 101, or 011 for a total of three ways which equals 3!/(2!1!). The number of ways that a set of occupation numbers n i can be realized is the product of the ways that each individual energy level can be populated: = (,) =!!
Every particle has a non-negative spin quantum number s. The number 2s is an integer, odd for fermions and even for bosons. Each s has 2s + 1 z-projection quantum numbers; σ = s, s − 1, ... , −s + 1, −s. [a] This is an additional discrete variable the wavefunction requires; ψ(r, t, σ).
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