Many-particle Systems
When turning to N-particle systems, i.e., systems containing N identical particles i.e. particles characterized by the same quantum numbers such as mass, charge and spin, is necessary an extension of single-particle state function to the N-particle state function . A fundamental difference between classical and quantum mechanics concerns the concept of indistinguishability of identical particles. Only two species of particles are thus possible in quantum physics, the so-called bosons and fermions which obey the rules:
(bosons),
(fermions).
Where we have interchanged two coordinates of the state function. The usual wave function is obtained using the slater determinant and the identical particles theory. Using this basis, it is possible to solve any many-particle problem.
Read more about this topic: First Quantization
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—Ivan Sergeevich Turgenev (1818–1883)