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The aim of this book is to give a comprehensive treatment of the
different methods for the construction of spin eigenfunctions and
to show their interrelations. The ultimate goal is the construction
of an antisymmetric many-electron wave function that has both
spatial and spin parts and the calculation of the matrix elements
of the Hamiltonian over the total wave function. The
representations of the symmetric group playa central role both in
the construction of spin functions and in the calculation of the
matrix elements of the Hamiltonian, so this subject will be treated
in detail. We shall restrict the treatment to spin-independent
Hamiltonians; in this case the spin does not have a direct role in
the energy expression, but the choice of spin functions influences
the form of spatial functions through the antisymmetry principle;
the spatial functions determine the energy of the system. We shall
also present the "spin-free quantum chemistry" approach of Matsen
and co-workers, in which one starts immediately with the
construction of spatial functions that have the correct
permutational symmetries. By presenting both the conventional and
the spin-free approach, one gains a better understanding of certain
aspects of the elec tronic correlation problem. The latest advance
in the calculation of the matrix elements of the Hamiltonian is the
use of the representations of the unitary group, so this will be
the last subject. It is a pleasant task to thank all those who
helped in writing this book."
The author wrote a monograph 20 years ago on the construction of
spin eigen functions; the monograph was published by Plenum. The
aim of that mono graph was to present all aspects connected with
the construction of spin eigen functions and its relation to the
use of many-electron antisymmetric wavefunc tions. The present book
is an introduction to these subjects, with an emphasis on the
practical side. After the theoretical treatment, there will be many
exam ples and exercises which will illustrate the different
methods. The theory of the symmetric group and its representations
generated by the different spin eigen functions is an other
subject, this is closely related to the quantum chemical
applications. Finally we will survey the calculation of the matrix
elements of the Hamiltonian, using the different constructions of
the spin functions. The closing chapter will deal with a new method
that gained much importance recently; the spin-coupled valence bond
method. Since the publication of Spin Eigenfunctions, nearly 20
years ago there have been many interesting developments in the
subject; there are quite a few new algorithms for the construction
of spin eigenfunctions. Moreover the use of the spin-coupled
valence bond method showed the importance of using different
constructions for the spin functions. The subject matter of this
book has been presented in a graduate course in the Technion. The
author is obliged to the graduate students Averbukh Vitali,
Gokhberg Kirill, and Narevicius Edvardas for many helpful
comments."
The author wrote a monograph 20 years ago on the construction of
spin eigen functions; the monograph was published by Plenum. The
aim of that mono graph was to present all aspects connected with
the construction of spin eigen functions and its relation to the
use of many-electron antisymmetric wavefunc tions. The present book
is an introduction to these subjects, with an emphasis on the
practical side. After the theoretical treatment, there will be many
exam ples and exercises which will illustrate the different
methods. The theory of the symmetric group and its representations
generated by the different spin eigen functions is an other
subject, this is closely related to the quantum chemical
applications. Finally we will survey the calculation of the matrix
elements of the Hamiltonian, using the different constructions of
the spin functions. The closing chapter will deal with a new method
that gained much importance recently; the spin-coupled valence bond
method. Since the publication of Spin Eigenfunctions, nearly 20
years ago there have been many interesting developments in the
subject; there are quite a few new algorithms for the construction
of spin eigenfunctions. Moreover the use of the spin-coupled
valence bond method showed the importance of using different
constructions for the spin functions. The subject matter of this
book has been presented in a graduate course in the Technion. The
author is obliged to the graduate students Averbukh Vitali,
Gokhberg Kirill, and Narevicius Edvardas for many helpful
comments."
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