Natural spectrum of a charged quantum oscillator

Summary

The spectrum of a harmonically bounded electron is investigated, which couples to its own radiation field. For the coupling, an appropriately simplified version of the minimal electromagnetic coupling is used. This system is treated exactly by path integration. By integrating out the field variables, a reduced system is obtained, which depends only on the electron variables. It is regarded as a model for thenatural charged quantum oscillator. The interaction of the oscillator with the field is condensed in a non-local potential for the electron, and the present investigations concern the modifications of the oscillator spectrum due to this additional potential. An analytic formula for the whole spectrum is obtained as the inverse Laplace transform of the partition function. The properties of the spectrum are studied in detail and are related to the radiative behaviour of the system. In particular, it is shown that the shapes of the broadenend spectral lines differ slightly from Lorentz profiles proving that the spontaneous decays of the states are not purely exponential. The widths and shifts of the lines are computed. It is mentioned that the model is rather universal so that the results apply, in principle, to other dissipative systems.