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Advanced Quantum Mechanics by Jeroen Danon, Yuli V. Nazarov

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2 Identical particles

We are now ready for new material. In this chapter we consider systems which contain not just one or two particles, but any (large) number of particles. After presenting the Schrödinger equation for a general N-particle system, we focus on the case where all N particles are identical. For a classical system this would have no special implications, it would just mean that all particles have equal properties like charge, mass, etc. For a quantum system, however, we show that the situation is completely different: most solutions of the Schrödinger equation for a system of identical particles are redundant – they cannot occur in nature. The physical solutions of the Schrödinger equation are either completely symmetric with respect ...

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