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Hamilton's optico-mechanical analogy is a concept of classical physics enunciated by William Rowan Hamilton.〔Hamilton, W.R., (1834).〕 It may be viewed as linking Huygens' principle of optics with Jacobi's Principle of mechanics.〔Kemble, E.C. (1937), pp. 7–10.〕〔Lanczos, C. (1949/1970). Lanczos wrote on p. 136: "() ... thus pointed to that remarkable analogy between optical and mechanical phenomena which was observed much earlier by John Bernoulli and which was later fully developed in Hamilton's ingenious optico-mechanical theory. This analogy played a fundamental role in the development of modern wave-mechanics."〕〔Synge, J.L. (1954). On p. 2, Synge writes: "... the analogy between Newtonian mechanics and geometrical optics is completed only when we supplement the former by thinking of waves in association with the paths of particles. This completion was actually present in Hamilton's theory, since he made it so wide as to include both corpuscular and wave theories of light, and in the former interpretation his surfaces of constant action are the waves in question. Thus, since the time of Hamilton we have actually had what might be called 'Newtonian geometrical mechanics', based on the principle of Maupertuis, , where is given in terms of energy by ."〕〔Messiah, A. (1961), pp. 53–55.〕〔Arnold, V.I. (1974/1978), p. 252.〕 According to Cornelius Lanczos, the analogy has been important in the development of ideas in quantum physics.〔 According to Erwin Schrödinger, for micromechanical motions, the Hamiltonian analogy of mechanics to optics is inadequate to treat diffraction, which requires it to be extended to a vibratory wave equation in configuration space.〔Schrödinger, E. (1926/1928), p. ix.〕 ==Huygens' principle== The propagation of light can be considered in terms of rays and wavefronts in ordinary physical three-dimensional space. One may consider an inhomogeneous anisotropic medium with smoothly distributed properties that are described by an index of refraction that is a well-behaved function of position. Huygens' principle governs the propagation of a wavefront as it can be derived from Fermat's principle. The wavefronts are two-dimensional curved surfaces. The rays are one-dimensional curved lines.〔Arnold, V.I. (1974/1978), p. 250.〕 Thus, a wave is a foliated set of moving two-dimensional surfaces. In classical physics, it is not part of the definition of a wave that it be distinctly vibratory. One difference between wave and particle conceptions is thus in the spatial dimensionality of their moving objects. On one hand, a ray can be regarded as the orbit of a particle of light. It successively punctures the wave surfaces. The successive punctures can be regarded as defining the trajectory of the particle. On the other hand, a wave-front can be regarded as a level surface of displacement of some quantity, such as electric field intensity, hydrostatic pressure, particle number density, oscillatory phase, or probability amplitude. Then the physical meaning of the rays is less evident. This is wave–particle duality for a single particle in ordinary three-dimensional physical space or for a wave of some property of a medium with a spatial distribution of properties that is mostly continuous but not homogeneous. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hamilton's optico-mechanical analogy」の詳細全文を読む スポンサード リンク
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