Light optics, electron optics and wave mechanics

Abstract

IN 1831 William Rowan Hamilton discovered the analogy between the trajectory of material particles in potential fields and the path of light rays in media with continuously variable refractive index. By virtue of its great mathematical beauty, the ‘Hamiltonian Analogy’ survived in the textbooks of dynamics for almost a hundred years, but did not inspire any practical applications until 1925 when H. Busch first explained the focusing effect of electric and magnetic fields on electron beams in optical terms. Almost at the same time E. Schrodinger took the Hamiltonian Analogy a step further by passing from geometrical optics to wave optics of particles with his wave equation, in which he incorporated the wavelength of particles, first conceived by Louis de Broglie in 1923. Practical electron optics developed rapidly from 1928 onwards. By this time the Hamiltonian Analogy was widely known and inspired the invention of electron-optical counterparts of light-optical instruments, such as the electron microscope. Though the mathematical analogy is general, the two techniques are not exactly parallel. Some electron-optical instruments such as cathode-ray tubes and systems with curved optic axes have no important counterparts in light optics. In the available space only those problems of electron optics will be considered whose light-optical analogues were developed at length in the previous chapters of this work, so that the results can be transferred almost in toto, with few modifications. It may be noted that this applies in particular to the most recondite chapter of electron optics: the wave theory of lens aberrations.