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Spin-Free quantum chemistry. XVIII. The unitary group formulation of the many-electron problem

✍ Scribed by F. A. Matsen

Publisher
John Wiley and Sons
Year
1976
Tongue
English
Weight
555 KB
Volume
10
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

The representation of an N‐electron Schrödinger Hamiltonian on an orthonormal, spin‐free (freon) orbital product space is exactly modeled by a second‐degree polynomial in the infinitesimal generators of the unitary group. Symmetry adaptation of the orbital product space with respect to the symmetric group yields Gel'fand states which provide base for irreducible represntations of the unitary group. These exist in closed form as, in consequence, does the representation of the model Hamiltonian in this same basis. We retain as physical only those states characterized by tableaux with no more than two columns for which the spin labelling is one‐half the difference in the lengths of the two columns. The unitary group formulation is equivalent to standard, number‐conserving, second‐quantized, many‐body theory.

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On the structure of the Clifford algebra
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✍ Atri Mukhopadhyay 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 393 KB 👁 3 views

An attempt has been made to understand the structure of the Clifford algebra unitary group adapted many-particle states from the conventional symmetric group point of view. Emphasizing the symmetric group result that the consideration of the spin-independent Hamiltonian matrix over the many-particle