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Matter waves are neither transverse nor longitudinal. They do not represent any physical oscillations. Rather, their wave properties are only manifested by the fact that the likelyhood of a physical interaction in space can be described by the quantum mechanical wave function. This wave function allows for the matter waves to have a phase (but not a shape!) which allows for traditional wave properties like interference to arise.

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Q: Matter wave is transverse or longitudinal waves?
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