Theory of Excited States for Many-Electron Systems by Means of Variational Principles for Subspaces
In this paper the excitation spectrum of many-electron systems is discussed in terms of variational principles for subspaces. It is shown how these principles can be applied to derive Hartree-Fock type equations for excited states. In this scheme fractional occupation numbers appear. The theory of variational principles for subspaces is used to derive Slater’s transition state theory. This is achieved by showing that there is a one to one correspondence between the subspace spanned by the M lowest energy eigenstates and the sum of the densities of these eigenstates. Slater’s transition state theory comes out as a generalisation of the H-K-S theory for excited states. In this theory too fractional occupation numbers appear.
KeywordsIrreducible Representation Variational Principle Invariant Subspace Occupation Number Solid State Phys
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