Question

reconstruct the wave-function from one body reduced density matrix?

Answer 1

Hey dear here is your answer

.Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density matrix (2-RDM). We present a closed equation of motion for the 2-RDM by developing a reconstruction functional for the three-particle reduced density matrix (3-RDM) that preserves norm, energy, and spin symmetries during time propagation. We show that approximately enforcing N-representability during time evolution is essential for achieving stable solutions. As a prototypical test case which features long-range Coulomb interactions we employ the one-dimensional model for lithium hydride (LiH) in strong infrared laser fields. We probe both one-particle observables such as the time-dependent dipole moment and two-particle observables such as the pair density and mean electron-electron interaction energy. Our results are in very good agreement with numerically exact solutions for the N-electron wave function obtained from the multiconfigurational time-dependent Hartree-Fock method

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Answer 2

$<b>$Here is your answer

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➡️Due Hohenberg-Kohn theorem there is a bijective mapping between the diagonal of the reduced density matrix (just density) and the many body wave function.


➡️ So one has to "just" solve the inverse problem of finding the external potential which produces the density and then solve the many-body schrödinger equation for that external potential.


➡️ In practice of course this is never done like that......