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Energy of the interaction of atom and the radioactive field

Yuexin Liu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Through Hamilton’s operator,mathematic model was built systematically when atom and the radioactive field interact.By means of perturbation approximate method,the Schrodinger equation included time was solved and the systematic general energy was calculated.This article proves fatherly that it is a conservation of the sum of atom system and outside magnetic filed.

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Through Hamilton’s operator,mathematic model was built systematically when atom and the radioactive field interact.By means of perturbation approximate method,the Schrodinger equation included time was solved and the systematic general energy was calculated.This article proves fatherly that it is a conservation of the sum of atom system and outside magnetic filed.
The starting point in a quantum mechanical problem is the construction of a Schrödinger equation. A Schrödinger equation is exactly solvable only for a certain number of simple potentials. In most of the cases the Schrödinger equation can be solved exactly. The solution of the Schrödinger equation for the real systems is usually complicated and often exact solutions. The perturbation theory has been proven to be useful in several fields of theoretical physics and also in chemistry. It provides considerable insight into various phenomena. The main disadvantage of this method is that in certain problems the perturbation series converges slowly or diverges. The splitting of an energy level due to the interaction of the nuclear magnetic dipole and the magnetic field Be produced by the electron orbit current is called the fine structure. The term hyperfine structure is used to describe extremely small splitting of spectral lines.
In Chap. 1 we introduced the Schrodinger equation and gave solutions for a number of simple cases. The general solution was then obtained by a linear superposition of these solutions. In our work, we are particularly concerned with the way in which atomic systems interact with electromagnetic radiation. These systems are still described by wave functions given by superpositions of simple solutions, but the expansion coefficients Cn (probability amplitudes) become functions of time. In this chapter we derive equations of motion for the expansion coefficients using Schrddinger’s equation and introduce the electric-dipole interaction energy. Then, specializing to a two-level system and a monochromatic electromagnetic field, we solve the equations of motion both by time-dependent perturbation theory and by the more exact Rabi method.
The starting point in a quantum mechanical problem is the construction of a Schrödinger equation. We try to solve it exactly to obtain wave function. A Schrödinger equation is exactly solvable only for a certain number of simple potentials. In most of the cases the Schrödinger equation cannot be solved exactly. The solution of the Schrödinger equation for the real systems is usually complicated and often exact solutions are very difficult to find or solutions not exist. Examples include as anharmonic oscillator, hydrogen atom in an electric field, a plane rotator in the presence of an applied electric field and so on. Therefore, we need to rely on approximation methods. The simple and most interesting and powerful approximate method is the perturbation theory developed by Schrödinger in 1926 [1]. Earlier Lord Rayleigh [2] analysed harmonic vibrations of a string perturbed by small inhomogeneities. The work of Rayleigh was pointed out by Schrödinger. Consequently, the method is also called Rayleigh-Schrödinger perturbation theory. This method is powerful for determining the changes in the discrete energy values and the associated eigenfunctions of a system due to a weak perturbation, provided the eigenpairs of the undisturbed system are available. The approximations obtained from the perturbation theory are used to calculate energy level diagrams and to understand the splitting and assignments of atomic and molecular spectra [35]. The perturbation theory has been proven to be useful in several fields of theoretical physics and also in chemistry. It provides considerable insight into various phenomena. The main disadvantage of this method is that in certain problems the perturbation series converges slowly or diverges.
This chapter is devoted to an introduction to atomic physics which will be mainly concerned with one-electron atoms. After a brief discussion of the perturbation and variational methods in Section 14.1, in Section 14.2 we study the fine and hyperfine structure of the energy levels as well as the effect of a magnetic field on these levels. In Section 14.3 we examine the coupling of an atom to an electromagnetic field and important applications of this coupling such as the photoelectric effect and the rate of spontaneous emission. In Section 14.4 we give a brief introduction to a subject which has been expanding enormously in the last twenty years, the laser manipulation of atoms, and we discuss Doppler cooling and magneto-optical traps. Finally, Section 14.5 is devoted to a short discussion of two-electron atoms. Approximation methods Generalities In classical physics it is only in exceptional cases that it is possible to solve the Newton or Maxwell equations analytically given the initial conditions at time t = t 0 and, in the first case, the forces, or, in the second, the sources of electromagnetic field. In general, it is necessary to resort to an approximation method such as numerical integration of the equations, the perturbation method, or something else. The situation is no different in quantum physics: only in exceptional cases do we know how to “solve the Schrödinger equation” exactly, that is, how to obtain the time evolution of the state vector |ϕ( t 〉 as a function of its value |ϕ( t 0 〉 at initial time t = t 0 .