The reflection of hydrogen atoms from lithium fluoride期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The reflection of hydrogen atoms from lithium fluoride

Authors:	Thomas H Johnson

Abstract:	The paper describes the phenomena associated with the reflection of a sharply defined beam of hydrogen atoms from a crystal of LiF. Of primary interest is the fact that the atoms show interference effects in agreement with the wave mechanics theory and plane grating diffraction patterns are photographed. Evidence of the thermal agitation of the surface ions is obtained from the diffuse reflection with surrounds the specular beam.The Schrödinger wave equation for the motion of a free particle of mass m is $▽^{2} ψ ? 4πmi h ?ψ ?t = 0 (I)$ . The solution of this equation corresponding to the kinetic energy $mv^{2} 2$ is $ψ = Ae^{2πi(vt?σ_{x}x?σ_{y}y?σ_{x}z)}, (2)$ where $v  mv^{2} 2 and σ mv h$ . The motion of such a particle should have the characteristics of a plane wave of frequency ν and wave-length $λ = 1 σ$ . The experiments of various investigators¹ have shown the validity of the wave theory of the motion of the free electron and have given values of the wave-length in agreement with the theory.The free motion of atoms, ions and molecules should likewise have wave characteristics. In the case of the hydrogen atom, as the simplest example, the complete wave equation may be written in the form $I m ▽^{2} x,y,zψ + I μ ▽^{2} η,μζψ ? 8π^{2} μ?ψ mh^{2} η^{2} + μ^{2} + ζ^{2}$ $? 4πi h ?ψ ?t = 0, (3)$ where x, y, z, are the coördinates of the center of mass of the atom and ξ, η, ζ the coördinates of the electron with respect to the center of mass. If m_? and m₊ are the masses of electron and proton, m and μ have the significance $m = m_{?} + m_{+} and I μ = I m_{?} + I m_{+}$ . Equation (3) is solved by $ψ = U_{1} (x,y,z) U_{2} (η, ν ζ) ?^{2πiEth}$ , where E may have a continuous set of values and represents the total energy. U₁ and U₂ must satisfy the equations $▽_{1}^{2} U_{1} + 8π^{2} mβU_{1} h^{2} = 0, (4)$ and $▽_{2}^{2} U_{2} + 8π^{2} μ h^{2} (α ? μ? m η^{2} + ν^{2} + ζ^{2}) U_{2} = 0 (5)$ , where $α + β + E$ .

Keywords:
本文献已被 ScienceDirect 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏