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Acta Physica Sinica

Discussion on the transformation property between the configuration wavefunction of the equivalent-electron and the Young tableau

HU Kun-ming, 商丘师范学院物理与信息工程系，商丘 476000

Published Jan 1, 2005• 0 citations
Publisher

Abstract

The transformation property between the configuration wavefunction of the equivalent-electron and the Young tableau is pointed out to be unitary but not to be Hermite unitary. And a sign error of the spectrum item wavefunction is presented.
DOI
10.7498/aps.54.4524

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Quantum kinematics of the linear Heisenberg ring, consisting of N crystal nodes, each with spin s, is presented in terms of the Weyl duality between actions of the symmetric and unitary groups in the space of quantum states of the magnet. This space is spanned on magnetic configurations which gives rise to an application of the combinatorial Robinson–Schensted–Knuth algorithm for a unique classification of irreducible basis of the duality of Weyl in terms of a pair of tableaux: a standard Young tableau in the alphabet of nodes, accompanied by a semistandard Weyl tableau in the alphabet of spins. Similarities and distinctions between various group-theoretic and combinatorial objects are discussed within the context of the magnetic interpretation. In particular, the role of the spectrum of Jucys–Murphy operators in the clasification and construction of magnetic eigenstates corresponding to Young tableaux is illustrated.
The concepts of the basic symmetric operator and complete symmetric operator of the equivalent-electron regular Young tableau T［λ］ig are presented, and the concepts of the root state and generative state generated by these symmetric operators acting on each Slater function i are also given. Based on the establishment rules of the vertical permutation operator A［λ］ig of the orthogonal normalization Young tableau T［λ］ie, the symmetric operators in A［λ］ie and the equiprobability comparison method for solving T［λ］ie are presented, which can avoid the complicated algebra involving many operators. Finally, a new method for sloving the Young basis of the electron system with a large N is presented.