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Exact factorization ansatz of the ground state many-body wave function: A case study of quartic potential problem
Zhiyuan Yin1, Yi Deng1, Xinyao Wang1
1Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China.
The Journal of Chemical Physics
|August 29, 2025
Summary
Researchers developed an explicit factorized formula for many-body wave functions in quartic potentials. This method efficiently represents wave functions and calculates energy, offering insights into quantum mechanics.
Area of Science:
- Quantum Mechanics
- Computational Physics
Background:
- Solving the Schrödinger equation for many-body systems is computationally challenging.
- Existing methods like basis expansion can be inefficient for complex potentials.
Purpose of the Study:
- To propose an explicit factorized formula for the ground state many-body wave function.
- To demonstrate the efficiency of a novel method for solving Schrödinger equations.
Main Methods:
- Developed a new method for solving Schrödinger equations.
- Proposed an exact factorization ansatz for the many-body wave function.
- Applied the method to a model quartic potential in 2D and 3D.
Main Results:
- An explicit factorized formula for the ground state many-body wave function was derived.
- The formula features a non-integer pre-exponential factor, dominant decaying terms, and a modulator function.
- The method proved more efficient than basis expansion for wave function representation and energy calculation.
Conclusions:
- The proposed factorization ansatz offers a novel approach to understanding many-body wave functions.
- This method provides significant advantages over conventional techniques for specific quantum systems.
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