Initial value problem and causality of radiating oscillator

Abstract
The exact solution for the non-relativistic harmonic oscillator interacting with an electromagnetic field in the dipole approximation is derived with the help of the Heisenberg equation of motion. The space-time distribution of the field is reconstructed. The initial value problem for the field and for the motion of the oscillator is solved. The solutions obey macroscopic and microscopic causality conditions.

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