2003/09/09 by Xiao-Yin Pan, Pan, Xiao-Yin, Viraht Sahni +1
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.cond-mat/0309231
8 pages
arxiv created 2003/09/09 · arxiv updated 2009/12/01
For one-dimensional many-body systems interacting via the Coulomb force and with arbitrary external potential energy, we derive (i) the node coalescence condition for the wave function. This condition rigorously proves the following: (ii) that the particles satisfy only a node coalescence condition; (iii) that irrespective of their charge or statistics, the particles cannot coalesce; (iv) that the particles cannot cross each other, and must be ordered; (v) the particles are therefore distinguishable; (vi) as such their statistics are not significant; (vii) conclusions similar to those of the spin-statistics theorem of quantum field theory are arrived at via non-relativistic quantum mechanics; (viii) the noninteracting system cannot be employed as the lowest-order in a perturbation theory of the interacting system. (ix) Finally, the coalescence condition for particles with the short-ranged delta-function interaction and arbitrary external potential energy, is also derived. These particles can coalesce and cross each other.