A Bremsstrahlung single photon or spectrum

[gjj]

TL;DR Summary

A single collision between an electron and heavy ion produces a continuous range of frequencies in classical electrodynamics. In quantum electrodynamics that same situation produces a single photon. Which is it?

Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in terms of a distribution of frequencies. In Harris “A Pedestrian Approach to Quantum Field Theory” the same problem is attacked also in the non-relativistic case. Various approximations are used in both cases to make the calculations easier. The classical case results in a spectrum that consists of a continuous band of frequencies where each frequency band contributes roughly the same energy. The quantum case, in a first approximation produces a single photon of a given energy. Rybicki claims that both classical and quantum calculations are largely in agreement (a Gaunt factor makes the agreement better). How can there be agreement when we have a spectrum vs a single photon? Which is it, a spectrum or a photon? How do we show that a single photon has the Larmor energy predicted classically?

 

[nrqed]

Summary:: A single collision between an electron and heavy ion produces a continuous range of frequencies in classical electrodynamics. In quantum electrodynamics that same situation produces a single photon. Which is it?

Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in terms of a distribution of frequencies. In Harris “A Pedestrian Approach to Quantum Field Theory” the same problem is attacked also in the non-relativistic case. Various approximations are used in both cases to make the calculations easier. The classical case results in a spectrum that consists of a continuous band of frequencies where each frequency band contributes roughly the same energy. The quantum case, in a first approximation produces a single photon of a given energy. Rybicki claims that both classical and quantum calculations are largely in agreement (a Gaunt factor makes the agreement better). How can there be agreement when we have a spectrum vs a single photon? Which is it, a spectrum or a photon? How do we show that a single photon has the Larmor energy predicted classically?

Quantum field theory does not predict that there is a single photon emitted. There is an infinity, with the total energy spread among them.