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the claim
The non-relativistic Schrödinger equation can be derived as a limit of the Klein-Gordon equation
the verdict
SUPPORTED
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Recorded sources
6 sources for · 0 against
Is it true that the non-relativistic Schrödinger equation can be derived as a limit of the Klein-Gordon equation?
Yes. The claim that the non-relativistic Schrödinger equation can be derived as a limit of the Klein-Gordon equation is fully supported by multiple mathematical and physical analyses.
Verdict: SUPPORTED · 6 sources for, 0 against · Last checked
The analysis
The retrieved literature consistently confirms that under appropriate asymptotic limits (such as low frequency, low velocity, or taking the speed of light to infinity), both linear and nonlinear Klein-Gordon equations reduce to or can be approximated by the Schrödinger equation.
Evidence for · 6
The study demonstrates that the nonlinear Klein-Gordon equation can be approximated by nonlinear Schrödinger equations in the non-relativistic limit regime.
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Lu, Y. & Zhang, Z. (2017). Higher order asymptotic analysis of the Klein–Gordon equation in the non-relativistic limit regime. doi.org. https://doi.org/10.3233/asy-171414
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More for · 5
The work notes that the non-relativistic, quasi-static limit of the Klein-Gordon equation simply yields the Schrödinger equation under general conditions.
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Gourdain, P. -. (2025). The Klein-Gordon equation with relativistic mass: a relativistic Schrödinger equation. arxiv.org. https://doi.org/10.48550/arXiv.2501.07798
The research analyzes the low-frequency phase space regime where the Klein-Gordon equation is approximable by the usual Schrödinger equation.
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Hassell, A., Jia, Q., Sussman, E., & Vasy, A. (2025). Microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: Asymptotics. arxiv.org. https://doi.org/10.48550/arXiv.2511.08724
The study establishes robust global estimates showing the Klein-Gordon equation approaches the Schrödinger equation in the non-relativistic limit.
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Hassell, A., Jia, Q., Sussman, E., & Vasy, A. (2025). Microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: Estimates. arxiv.org. https://doi.org/10.48550/arXiv.2509.09518
The investigation proves that solutions to the cubic nonlinear Klein-Gordon equation converge to solutions of the cubic non-linear Schrödinger equation in the non-relativistic limit.
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Bambusi, D., Belloni, A., & Giuliani, F. (2025). Non relativistic limit of the nonlinear Klein-Gordon equation: Uniform in time approximation of KAM solutions. arxiv.org. https://doi.org/10.48550/arXiv.2501.17691
The paper confirms the non-relativistic limit of defocusing cubic nonlinear Klein-Gordon equations where modulated profiles are solutions to a Schrödinger equation.
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Lei, Z. & Wu, Y. (2023). Non-relativistic limit for the cubic nonlinear Klein-Gordon equations. arxiv.org. https://doi.org/10.48550/arXiv.2309.10235
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What does the evidence say?
The retrieved literature consistently confirms that under appropriate asymptotic limits (such as low frequency, low velocity, or taking the speed of light to infinity), both linear and nonlinear Klein-Gordon equations reduce to or can be approximated by the Schrödinger equation.
Receipt History
first checked31 Jul 2026
judged → SUPPORTED · 7731 Jul 2026
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