Derivation of the Landau-Zener formula via functional equations

• URL: http://arxiv.org/abs/2504.02576v1
• Date: Thu, 03 Apr 2025 13:40:25 GMT
• Title: Derivation of the Landau-Zener formula via functional equations
• Authors: Chen Sun,
• Abstract summary: We present a derivation of the Landau-Zener transition probability using a fundamentally different approach via functional equations.<n>Our work provides new insight into the origin of the exponential form of the Landau-Zener transition probability.
• Score: 7.157592602005623
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Landau-Zener formula describes the diabatic transition probability of a two-level system under linear driving. Its rigorous derivation typically relies on sophisticated mathematical tools, such as special functions, Laplace transforms, or contour integrals. In this work, we present a derivation of the Landau-Zener transition probability using a fundamentally different approach via functional equations. By leveraging integrability, we prove that this transition probability satisfies a functional equation, whose solutions establish the exponential form of the formula. The coefficient in the exponent is then determined through a lowest-order perturbation calculation. This derivation is rigorous and mathematically simple. Our work provides new insight into the origin of the exponential form of the Landau-Zener transition probability.

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