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Hartree-fock approximation for inverse many-body problems

¹Institut fur Theoretische Physik I, Universitat Munster, 48149 Munster, Germany.

Physical Review Letters

|September 16, 2000

Summary

This study introduces a novel computational method to reconstruct quantum potentials from observational data. The approach combines Bayesian statistics and Hartree-Fock approximation for feasible analysis of many-body systems.

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Area of Science:

Quantum mechanics
Computational physics
Statistical inference

Background:

Reconstructing quantum potentials from observational data is a challenging inverse problem.
Existing methods may lack computational feasibility or a general framework for complex many-body systems.

Purpose of the Study:

To present a novel, computationally feasible method for reconstructing quantum mechanical many-body system potentials.
To establish a general framework for addressing inverse problems in quantum many-body systems.

Main Methods:

A nonparametric Bayesian approach is combined with the Hartree-Fock approximation.
A priori information is incorporated as a stochastic process defined on the space of potentials.

Main Results:

The proposed method is computationally feasible.
It provides a general framework for reconstructing quantum potentials from observational data.

Conclusions:

The new method offers a practical and versatile approach to solving inverse problems in quantum many-body systems.
This work advances the ability to infer system properties from experimental or simulated data.

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