Nonspurious Basis Set for the Study of Many-Body Problems in a High Magnetic Field and Harmonic Potential

Abstract We introduce a method for constructing a nonspurious N -body wave function of electrons in a high magnetic field and harmonic potential with a well-defined permutational symmetry. We derive closed form expressions for the matrix elements of two- and three-body operators in this basis set. As an instructive example we carry a variational calculation of the ground state energy of noninteracting anyons in a high magnetic field and harmonic potential for a small statistical parameter. The evaluation is carried out by using an appropriate nonspurious fermionic basis set. Computational results are presented for systems of up to six anyons. It is shown that in the limit of a high magnetic field the energy spectrum is quadratic in the statistical parameter for any number of anyons. The numerical results suggest that the energy spectrum is roughly proportional to the inverse of the total angular momentum.