Formulas of standard Young tableaux for symmetric spatial wavefunctions of identical electrons

Hu Kun

Published Jan 1, 2000• 0 citations

Abstract

For n identical particles of electrons,the spatial configurations ( l f +l g - )with the given permutation symmetry are expressed in terms of n λ standard Young tableaux T [λ] i .The spatial wavefunction  1 of the n electron system related T [λ] 1 is Changed to the non perturbation function  1e .From the hypothesis of equal probability for spatial exchange between electrons with the opposite spins,the operator q +e related to T [λ] 1 is determined,the analytic forms of the non perturbation wavefunctions with the given permutation symmetry are derived,and the formulas for the symmetric spatial wavefunctions of identical electrons are obtained in terms of the Standard Young Tableaux.

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Formulas of standard Young tableaux for symmetric spatial wavefunctions of identical electrons

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Published Jan 1, 2000• 0 citations

OpenAlex

Abstract

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It is shown that the symmetry under parity of the wavefunctions of two identical particles with an arbitrary spin

s

in three spatial dimensions accounts for the appropriate wavefunction exchange statistics under the permutations of particles. The standard properties of the angular momentum in non-relativistic quantum mechanics account for the sign factor

(-1)^{2s}

that the wavefunctions acquire under the permutation of coordinates of the two particles, without any additional requirements, directly relating spin and the particle exchange statistics in the non-relativistic context.

N=2

and

N=3

identical interacting particles.