In the quantum mechanical approach we study the minimal length effect on Rayleigh scattering and Thomson scattering. We modify the usual Hamiltonian for the motion of an electron in a quantized electromagnetic radiation field by utilizing deformed operators to get the Hamiltonian with a minimal length. We derive expressions for modified Rayleigh scattering and modified Thomson scattering. Using appropriate experimental inputs we get the upper bounds on the deformation parameter and minimal length. The upper bound on the minimal length is less than the electroweak scale.

中文翻译：

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关于广义量子散射理论：最小长度的瑞利散射和汤姆森散射

在量子力学方法中，我们研究了最小长度对瑞利散射和汤姆森散射的影响。通过利用变形算子获得具有最小长度的哈密顿量，我们修改了电子在量子化电磁辐射场中运动的通常的哈密顿量。我们推导了修正的瑞利散射和修正的汤姆森散射的表达式。使用适当的实验输入，我们可以得出变形参数和最小长度的上限。最小长度的上限小于电弱标度。