Abstract
The suitable choice of a body-fixed frame of reference (BFR) is an essential point in the treatment of systems with identical particles. Starting from the fact that there exists a “best” BFR (“specific decoupling”), in which the wave function is a product of an internal and a collective part, we show that the collective term has to be invariant under permutations of the particles. On the other side in symmetrical configurations the BFR has to jump in a well-defined manner under those permutations which are equivalent to spatial rotations. It is shown that for non-symmetrical configurations the BFR must have the same properties. For 3 identical particles it is possible to construct in a purely geometrical way a BFR which has the right behaviour under particle permutations. The Hamiltonian in that BFR is derived and the connection with the “best” BFR is discussed.
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