The waves of an electron

Huawang Li

De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.

Ernesto Mazzucato

LASZLO SOLYMAR, Donald Walsh, R.R.A. Syms

Abstract Introduces the Schrödinger wave equation as the key equation governing the behaviour of electrons, and presents simple solutions (known as wave functions) as electron waves, and packets of electron waves, which can represent localised, particle-like electrons. Considers the behaviour of electron waves on meeting a potential barrier and trapped in potential wells with finite and infinite walls, and introduces the idea of energy levels. Discusses the accepted interpretation of the electron wave function, namely that its modulus square leads to the probability of finding an electron in a given region of space. Considers further the uncertainty relationship and associated philosophical implications.

Franklin F. Y. Wang

Carlos I. Calle

The major problem that physicists were trying to solve was that of the wave nature of the electron. In 1926, the Austrian physicist Erwin Schrodinger presented an equation that described the wave behavior of the electron in the hydrogen atom. The physicist Max Born suggested instead that these waves were waves of probability; that is, they represented the probability of finding the electron in some region of space. In fact, an electron has a well-defined position only when it is being observed. Position is not an intrinsic property of an electron. The wave nature of electrons is the basis for the electron microscope, invented in 1932 by Ernst Ruska in Germany. Electron wavelengths are much shorter than those of visible light.

Clinton J. Davisson