Deep Neural Network Approach Solves Dirac Equation

Researchers from Jilin University have made a significant breakthrough in solving the Dirac equation, a fundamental problem in quantum mechanics. Using a deep neural network and an unsupervised machine learning technique, the team was able to accurately solve the equation not only for the ground state but also for low-lying excited states. The research has been peer-reviewed and published in The European Physical Journal A.

Key Takeaways:

• The research uses a deep neural network and an unsupervised machine learning technique to solve the Dirac equation, which is a fundamental problem in quantum mechanics.
• The method proposed by the researchers can accurately solve the equation for both the ground state and low-lying excited states.
• The validity of the method is verified by calculations using the Coulomb and Woods-Saxon potentials.
• The research has been peer-reviewed and published in The European Physical Journal A.
• The study's authors include Jian Li, Chuanxin Wang, Tomoya Naito, and Haozhao Liang.
• The research was supported by the National Natural Science Foundation of China (NSFC), the RIKEN Special Postdoctoral Researcher Program, and the Japan Society for the Promotion of Science.

Statistics:

• The paper is published in The European Physical Journal A, Volume 61, Issue 7.
• The study's authors include 4 researchers from Jilin University.
• The research was supported by 4 funding organizations in China and Japan.
• The method proposed by the researchers can accurately solve the Dirac equation for both the ground state and low-lying excited states.

Sources:

• A Deep Neural Network Approach To Solve the Dirac Equation. The European Physical Journal A, 2025;61(7).
• NewsRx. New Networks Study Findings Have Been Reported by Researchers at Jilin University (A Deep Neural Network Approach To Solve the Dirac Equation). Journal of Engineering. August 11, 2025; p 1917.