Solutions to the Schrödinger equation using deep neural networks for integrated photonics
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Abstract
This paper introduces a novel method for solving the Schrödinger equation through the use of deep neural networks (DNNs), presenting a significant departure from traditional techniques. Conventional approaches to solving the Schrödinger equation, such as analytical methods and numerical algorithms, often face challenges when dealing with complex quantum systems due to their inherent limitations. These traditional methods can become cumbersome or even infeasible as the complexity of the systems increases. In contrast, our approach harnesses the capabilities of deep neural networks to approximate both the wavefunction and the energy eigenvalues of quantum systems. By leveraging the flexible and powerful nature of DNNs, we provide a new pathway to solving the Schrödinger equation that can potentially overcome the constraints of classical methods. To validate the effectiveness of our approach, we apply it to the particle in a box problem – a fundamental quantum mechanics model with well-established analytical solutions. This benchmark problem serves as a useful test case, allowing us to demonstrate that DNNs can not only replicate the known results accurately but also offer insights into how these networks can handle more intricate quantum systems. Our results reveal that DNNs are capable of accurately reproducing the analytical solutions for the particle in a box, illustrating their potential as a versatile tool for quantum mechanics.
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Research ethics: NA.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: Some part of the manuscript is checked for grammatical corrections.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: NA.
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Data availability: NA.
References
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- Multi-surveillance detection for night surveillance using modified yolo v5 algorithm based optical communication
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- Splice loss in dual mode triangular index fibers: an analytic approach in the presence of nonlinearity for various V numbers
- Performance signature for angular misalignment measurement of fiber to fiber connectors with minimum insertion loss and low distortion in optical fiber transceiver systems
- Networks
- Historical development of passive optical network (PON): a review
- Long wavelength fluoride optical glass fibers performance signature in high speed local area data networks
- Fairness optimized based DBA for long reach XGPON networks
- Systems
- Visible light communication optical FBMC-OQAM PAPR reduction using FHT-PTR algorithm for beyond 5G system
- Nonlinearity-tolerant transmission using modified phase-conjugate twin wave for M-PSK signals
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- Coherent optical-OFDM system’s contribution to the management of chromatic and polarization mode dispersion using DSP
- Enhancing the signal efficiency and PAPR performance of FBMC waveform in optical communication
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- Solutions to the Schrödinger equation using deep neural networks for integrated photonics
- Secrecy and performance analysis of dual hop FSO-RF system using differential chaos shift keying
- Joint PAPR reduction with channel estimation for OFDM-based VLC systems
