Matter waves of various particles - do they interact?

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San K
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this has been asked by someone before, though, but, i think, never got answered

can the matter waves of, say, a photon, interact with the matter waves of, say, an electron?

matter waves = de Broglie waves


lets say we have two pairs of double slits...a photons is sent through one pair and an electron is sent through the other

the pairs (of double slits) are now brought closer ...till the right slit of the photon and the left slit of the electron are within the wavelength of photon/electron...

would we observe an interference pattern indicating some sort of interference between the photon-matterwave and the electron-matterwave?
 
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Can you prepare any particle which cannot described by a wave function?
They can interact, and might modify your interference pattern.