Generalized variational principle for the time-dependent Hartree-Fock equations for a Slater determinant

Area of Science:

• Quantum mechanics
• Computational chemistry
• Theoretical physics

Background:

• The standard mean-field approach in quantum mechanics often simplifies interactions.
• Accurate energy calculations are crucial for understanding complex N-body systems.
• Variational methods are widely used to approximate solutions in quantum mechanics.

Purpose of the Study:

• To derive time-dependent Hartree-Fock equations from a general N-body variational principle.
• To investigate the nature and significance of time-dependent corrections to mean-field interactions.
• To develop a more accurate mean-field approach for calculating total interaction energy.

Main Methods:

• Derivation of time-dependent Hartree-Fock equations via a variational principle applied to an N-body action.
• Generalization of existing variational treatments based on reduced two-body actions.
• Analysis of self-consistent field equations to identify time-dependent corrections.

Main Results:

• The derivation successfully yields time-dependent Hartree-Fock equations.
• New time-dependent corrections to standard mean-field interactions are identified.
• A time-dependent phase shift for the Slater determinant is obtained, accounting for total interaction energy.

Conclusions:

• The derived variational principle offers a more rigorous foundation for time-dependent Hartree-Fock theory.
• The identified time-dependent corrections are physically significant for accurate mean-field calculations.
• The approach provides a method to properly include total interaction energy within the mean-field approximation.