Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.24194 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916767372148736 |
|---|---|
| author | Wu, Yi-Qiang Liu, Xuan Li, Hanlin Wang, Fuqiang |
| author_facet | Wu, Yi-Qiang Liu, Xuan Li, Hanlin Wang, Fuqiang |
| contents | Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving the one-dimensional time-independent Schrödinger equation to obtain ground- and excited-state wave functions, as well as energy eigenvalues by incorporating an embedding layer to generate process-driven data. The method demonstrates high accuracy for several well-known potentials, such as the infinite potential well, harmonic oscillator potential, Woods-Saxon potential, and double-well potential. Further validation shows that the method also performs well in solving the radial Coulomb potential equation, showcasing its adaptability and extensibility. The proposed approach can be extended to solve other partial differential equations beyond the Schrödinger equation and holds promise for applications in high-dimensional quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy-Embedded Neural Solvers for One-Dimensional Quantum Systems Wu, Yi-Qiang Liu, Xuan Li, Hanlin Wang, Fuqiang Computational Physics Quantum Physics Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving the one-dimensional time-independent Schrödinger equation to obtain ground- and excited-state wave functions, as well as energy eigenvalues by incorporating an embedding layer to generate process-driven data. The method demonstrates high accuracy for several well-known potentials, such as the infinite potential well, harmonic oscillator potential, Woods-Saxon potential, and double-well potential. Further validation shows that the method also performs well in solving the radial Coulomb potential equation, showcasing its adaptability and extensibility. The proposed approach can be extended to solve other partial differential equations beyond the Schrödinger equation and holds promise for applications in high-dimensional quantum systems. |
| title | Energy-Embedded Neural Solvers for One-Dimensional Quantum Systems |
| topic | Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2505.24194 |