Eigen symmetrical and antisymmetric functions of non-localized objects

Eigen symmetrical and antisymmetric functions of non-localized objects 

Let us consider a collection of N objects with weak interactions between one another. Schrbdinger s equation for the ensemble of the collection will be  

This ensemble corresponds to a series of N eigenfunctions obtained by permutation (see Appendix 3, section A3.4.2) of objects 1, 2,. .. iVbetween the indices of eigenvalues a, r,. ..co. An example of such a function would be  

For systems respectively degeneratedgcr.gr,---, g times, the total number of eigenfunctions will be N g g. ga - 

A series of A/ /% + +... + nj. eigenfunctions obtained by permutations exists, an example of which would be  

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