Summary: We construct the independent bases on the spatial wavefunction of four-identical-particle systems classified under the rotational group \(SO(3)\) and the permutation group \(S_{4}\) with the usage of transformation coefficients that relate wavefunctions described in one set of internal coordinates with those in another. The basis functions for \(N \leq 2\) are presented in the explicit expressions based on the harmonic oscillator model. Such independent bases are supposed to play a key role in the construction of the wavefunctions of the five-quark states and the variation calculation of four-body systems. Our prescription avoids the spurious states and can be programmed for arbitrary \(N\).{
©2013 American Institute of Physics}