Abstract

The time rate of energy emission in three quantum simple systems - the hydrogen atom, electron particle in a one-dimensional potential box and harmonic oscillator - has been calculated in two ways. The first one, based on the dipole approximation for the emitted energy, refers to classical electrodynamics. The other way is corresponding to quantum transitions of a single electron between definite energy levels. In this case the time of any transition is obtained by applying the Joule law characteristic for the dissipation of energy. The intensity of quantum transitions is found to be by several orders higher than the classical ones.

Highlights

  • According to classical electrodynamics any moving charged particle emits an amount of its energy during any time interval of its motion

  • In appendix A we show how (33) can be coupled with the quantum-mechanical calculations

  • By comparing (40,42,44) respectively with (46-48) we find that the quantum emission rate is in general by many orders larger than the classical rate

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Summary

Introduction

According to classical electrodynamics any moving charged particle emits an amount of its energy during any time interval of its motion. In the case of the orbits corresponding to higher energies the motion on them can exist for some rather long time, but - at some moment which remains undefined for an observer - the position of the electron may be changed to the orbit of a lower energy. This effect is connected with a sudden emission of energy the amount of which is equal to the energy difference between the higher and lower orbit states. If the end level is not a ground state, another emission process can take place afterwards at some unknown moment of time

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