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Journal of Yueyang Normal University

THE FEATURES OF ELECTRON POSITION MEANS OF TWO ENERGY LEVELS ATOM IN THE RADIATION FIELD

Yuexin Liu

Published Jan 1, 2001• 0 citations
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Abstract

Based on the quantum mechanics theory,by means of pertubation method this article derives the changing formula of electric dipole moment of two energy levels atom in the radiation field ,so as to study its features of electron position and get the conclusion that the electron position mean of atom in the radiation field is similar with an excited damping harmonic oscillator.

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Based on the quantum mechanics theory,by means of pertubation method this article derives the changing formula of electric dipole moment of two energy levels atom in the radiation field ,so as to study its features of electron position and get the conclusion that the electron position mean of atom in the radiation field is similar with an excited damping harmonic oscillator.
Suppose that the state of a single atom is described by two wave functions, then there is time-varying electric dipole moment and current in an atom staying in an energy eigen state. Using this time-varying electric current, we can use cla(?)sical electromagnetic theory to calculate the absorption and emission by the atom in a field and to calculate the spontaneous emission of this atom. The description of the usual quantum mechanics can be obtained by averaging our theory over the phase parameter.
In this paper, we have studied the Maxwell radiation from the electron orbiting the nucleus in an atom such as hydrogen atom. The orbiting electron is thought as two oscillating dipoles: one on [Formula: see text]-axis and the other on [Formula: see text]-axis with the same frequency. We have derived the electromagnetic wave and calculated powers of the radiation from these two oscillating dipoles, and then determined the time period it takes for the electron to change its energy levels from [Formula: see text] to [Formula: see text] due to the Maxwell radiation. Compared the time period due to the Maxwell radiation with the time period from the uncertainty principle, it is found that the two time periods are different from each other by about nine orders of magnitude. So, we are led to believe that the Maxwell theory could not be used in the quantum photo emission by the electron in an atom. Thus, we suggest that the quantum photo emission by the electron in an atom may be photon tunneling from the electron [Formula: see text] in an atom.
Abstract In a recent paper Schott has criticized the quantum mechanical method of finding the intensities of spectral lines, and in particular the assumption that the intensity may be derived by treating the atom as a dipole, radiating classically. The electric moment of this dipole is taken as p = e-2πivt ∫ Ψ*frΨidτ + Conjugate complex, (1A) where Ψi and Ψf are the wave functions of the initial and final states of the atom respectively, and in the Quantum Theory the usual assumption is that the energy radiated per unit time is given by R = 2 |p¨¯|2/3c2, (1B) where p¨¯ is the time average of p¨. A more consistent method is suggested in which the electric density ρ and the current j, corresponding to the transition, are found, and the electromagnetic field due to these two is examined.
Abstract The new quantum mechanics could at first be used to answer questions concerning radiation only through analogies with the classical theory. In Heisenberg’s original matrix theory, for instance, it is assumed that the matrix elements of the polarisation of an atom determine the emission and absorption of radiation analogously to the Fourier components in the classical theory. In more recent theories a certain expression for the electric density obtained from the quantum mechanics is used to determine the emitted radiation by the same formulæ as in the classical theory. These methods give satisfactory results in many cases, but cannot even be applied to problems where the classical analogies are obscure or non-existent, such as resonance radiation and the breadths of spectral lines. A theory of radiation has been given by the author which rests on a more definite basis. It appears that one can treat a field of radiation as a dynamical system, whose interaction with an ordinary atomic system may be described by a Hamiltonian function. The dynamical variables specifying the field are the energies and phases of its various harmonic conrponents, each of which is effectively a simple harmonic oscillator. One must, of course, in the quantum theory take these variables to be q-numbers satisfying the proper quantum conditions. One finds then that the Hamiltonian for the interaction of the field with an atom is of the same form as that for the interaction of an assembly of light-quanta with the atom. There is thus a complete formal reconciliation between the wave and light-quantum points of view.