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The quasiparticle (QP) energies, which are minus of the energies required byremoving or produced by adding one electron from/to the system, correspondingto the photoemission or inverse photoemission (PE/IPE) spectra, are determinedtogether with the QP wave functions, which are not orthonormal and even notlinearly independent but somewhat similar to the normal spin orbitals in thetheory of the configuration interaction, by self-consistently solving the QPequation coupled with the equation for the self-energy. The electron density,kinetic and all interaction energies can be calculated using the QP wavefunctions. We prove in a simple way that the PE/IPE spectroscopy and thereforethis QP theory can be applied to an arbitrary initial excited eigenstate. Inthis proof, we show that the energy-dependence of the self-energy is not anessential difficulty, and the QP picture holds exactly if there is norelaxation mechanism in the system. The validity of the present theory for someinitial excited eigenstates is tested using the one-shot GW approximation forseveral atoms and molecules.

A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates