Paraxial light and atom optics are compared. To lowest order the slowly varying amplitude of a light field in a dielectric medium with a spatially dependent refractive index satisfies an equation which has the form of a Schr\"odinger equation: the ``optical Schr\"odinger equation.'' The unsystematic procedure of neglecting certain second-order derivatives is replaced by a systematic expansion which allows the calculation of consecutive corrections. The general theory is applied to harmonic motion in a graded index fiber and to tunneling between coupled fibers. The physical relations between wave evolution of massive particles and paraxially propagating waves are elucidated.
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Marte et al. (1997) studied this question.
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