Double Slit FIG.:Double II.STATISTICAL INTERPRETATION OF WAVE MECHANICS aves 3 made is hypothesis ectrons.r ons.etc. around stal Wave function is a complex function of its variables (红，t)=Ae-B到) v(r0.00-Viogze-t 1.Dynamical equation governing the motion of micro-particle is by itself a equation containing imaginary number This able the app be of space is ible fr A.Pose of the problem What kind of wave it is? .Optics:Electromagnetic wave wave propagating E(红，t)=oe(-2叫=%-网 Eo-amplitudefield strength Intensity E-energy density ·Acoustic wave U(,t)foloe(2) 5 FIG. 2: Double slit experiments. II. STATISTICAL INTERPRETATION OF WAVE MECHANICS People tried hard to confirm the wave nature of micro-particles, and electron waves were first demonstrated by measuring diffraction from crystals in an experiment by Davison and Germer in 1925. They scattered electrons off a Nickel crystal which is the first experiment to show matter waves 3 years after de Broglie made his hypothesis. Series of other experiments provided more evidences, such as the double slit experiments using different particle beams: photons, electrons, neutrons, etc. and X-ray (a type of electromagnetic radiation with wavelengths of around 10−10 meters). Diffraction off polycrystalline material gives concentric rings instead of spots when scattered off single crystal. Wave function is a complex function of its variables ψ(x, t) = Ae i ~ (px−Et) ψ (r, θ, ϕ, t) = 1 √ πa3 0 e − r a0 e − i ~ E1t 1. Dynamical equation governing the motion of micro-particle is by itself a equation containing imaginary number 2. The wave function describing the state of micro-particle must fit the general theory frame of quantum theory (operator formalism) - requirement of homogeneity of space. This means, the symmetry under a translation in space r → r + a, where a is a constant vector, is applicable in all isolated systems. Every region of space is equivalent to every other, or physical phenomena must be reproducible from one location to another. A. Pose of the problem What kind of wave it is? • Optics: Electromagnetic wave E(x, t) = ˆy0E0e i( 2π λ x−2πνt) = ˆy0E0 wave propagating z }| { e i(kx−ωt) E0 − amplitude → field strength Intensity E 2 0 → energy density • Acoustic wave U(x, t) = ˆy0U0e i( 2π λ x−2πνt)