A matter wave thought experiment concerning Galilean transformations

Yamaguchi Takeshi, Tokyo Institute of Technology

The Schrödinger equation is invariant under Galilean transformations. Therefore, a matter wave should undergo the Doppler effect in the same manner as a classical wave and it should be observed when the measurement apparatus, i.e., the interferometer, moves with some velocity in the laboratory reference frame. Similarly, wave-like characteristics can be expected to appear if the measurement apparatus moves with the same velocity relative to the original particle, despite the fact that the particle is at rest in the laboratory reference frame. This paper provides a proposal for a simple thought experiment related to the reference frame dependence of the wave-particle duality using current matter wave optics technology. Full text


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