By Giampiero Esposito et al.

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The bottom two ﬁgures describe scattering of 75 V electrons from several large nickel crystals (Davisson and Germer 1927, c the American Physical Society). out. One then associates a wavelength with the incident electron beam, h of wave which turns out to be in good agreement with the value mv mechanics (see also chapter 4). The experimental apparatus used by Davisson and Germer consists of an electron gun G, a target T and a double Faraday box collector C. The electrons of the primary beam are emitted thermally from a tungsten ribbon F , and are projected from the gun into a ﬁeld-free enclosure containing the target and collector; the outer walls of the gun, the target, the outer box of the collector and the box enclosing these parts are always held at the same potential.

The problem of solving the Hamilton equations is then replaced by the analysis of a partial diﬀerential equation known as the Hamilton– Jacobi equation. In the time-dependent formulation, the solution is given by the Hamilton principal function, which leads, in turn, to the solution of the original problem for given initial conditions. If the Hamiltonian does not depend explicitly on time, however, it is more appropriate to re-express the Hamilton–Jacobi equation in a form that is solved by the Hamilton characteristic function.

A liquid-air bottle exploded at a time when the target was at high temperature. Thus, the experimental tube was broken, and the target was heavily oxidized by the inrushing air. Interestingly, when the experiments were continued (after reducing the oxide and removing a layer of the target), Davisson and Germer found that the angular distribution of the scattered electrons had been completely changed. e. the directions in which the atoms in the lattice are arranged along the smallest number of lines per unit area.