In this paper a detailed, rigorous mathematical analysis that confirms the Einstein’s hypothesis of the light quantum energy is presented. Moreover, the analysis shows that photon energy cannot be dependent on any other physical quantity but its frequency. In contrast to the Einstein’s thermodynamic approach to the black–body radiation and its analogy to the ideal gas, the presented analysis starts only from the assumption that the electromagnetic radiation is quantized. Relaying on the first principle and taking into account the Lorentz transformations properties it was found that photon energy is directly proportional only to the frequency of the electromagnetic radiation.

中文翻译：

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光子能量是否可能取决于频率以外的任何其他物理参数？

在本文中，我们进行了详细而严格的数学分析，证实了爱因斯坦关于光量子能量的假设。此外，分析表明，光子能量不能依赖于任何其他物理量，而是依赖其频率。与爱因斯坦对黑体辐射的热力学方法及其与理想气体的类比相反，本文提出的分析仅从电磁辐射被量化的假设开始。基于第一原理，并考虑到洛伦兹变换性质，发现光子能量仅与电磁辐射的频率成正比。