Conditions under which a quantum particle can be described using classical quantities are studied. We investigate the wavefunction of a quantum particle submitted to a potential field for which all quantum effects vanish, even if Planck's constant is non-negligible. This problem is equivalent to the problem of the motion of a particle in a refringent medium. The indices of refraction of such media are found. In these media, quantum particles have classical momenta, while their wave properties are described by the wave-optics equation with a characteristic length equal to the de Broglie wavelength ƛ. In the 1D case, the particle cannot be found in the region near the origin, since the index of refraction tends to infinity there. For the 3D case with central symmetry, the wave properties are determined by a function that has a resonance of width about 2ƛ. Experimental verification of theoretical predictions is discussed.

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