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Undergraduate lecture notes in physics

Identical Particles

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq, Gage Eichman, Abhishek Kumar Singh, Gabrielle Prime

Published Jan 1, 2023• 0 citations
Publisher
DOI
10.1007/978-3-031-37073-1_7

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Scattering is an important phenomenon of microscopic particle's interaction. The identical particles are the particles with inherent identical character in mass,electric charge,spin,etc. They show some special characteristic in their scattering. In this paper,the identical particles' scattering has been analysed from the symmetry of wave function, scattering cross - section and probabiliy. A comparison is made betwwen scattering of the identical particles and that of the non - identical particles.

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We consider entanglement in a system with a fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle basis chosen. The nonfactorization due to (anti)symmetrization is naturally excluded by using the (anti)symmetrized basis or, equivalently, the particle number representation. The natural degrees of freedom in quantifying the identical-particle entanglement in a chosen single-particle basis are occupation numbers of different single-particle basis states. The entanglement between effectively distinguishable spins is shown to be a special case of the occupation-number entanglement.

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Identical Particles

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Scattering is an important phenomenon of microscopic particle's interaction. The identical particles are the particles with inherent identical character in mass,electric charge,spin,etc. They show some special characteristic in their scattering. In this paper,the identical particles' scattering has been analysed from the symmetry of wave function, scattering cross - section and probabiliy. A comparison is made betwwen scattering of the identical particles and that of the non - identical particles.
We consider entanglement in a system with a fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle basis chosen. The nonfactorization due to (anti)symmetrization is naturally excluded by using the (anti)symmetrized basis or, equivalently, the particle number representation. The natural degrees of freedom in quantifying the identical-particle entanglement in a chosen single-particle basis are occupation numbers of different single-particle basis states. The entanglement between effectively distinguishable spins is shown to be a special case of the occupation-number entanglement.