An exactly solvable non-uniform electron trajectory yields classical radiation whose spectrum is precisely one-dimensional Planck, defining temperature T = ħκ/(2π k_B c).
An advanced undergraduate derivation of acceleration thermality
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abstract
The thermal radioactivity of beta-decay photons, described by a 1D Planck distribution, can be modeled as classical radiation emitted by an accelerated electron. Here, we present the basics of the out-of-equilibrium computation to illustrate acceleration thermality. Suitable for advanced undergraduate calculations, we demonstrate that an exactly soluble non-uniformly accelerated trajectory enables spectral analysis of the emitted photons, facilitates time evolution, and reveals Planckian radiation.
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An advanced undergraduate derivation of acceleration thermality
An exactly solvable non-uniform electron trajectory yields classical radiation whose spectrum is precisely one-dimensional Planck, defining temperature T = ħκ/(2π k_B c).