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When scientists fire a string of single particles rather than a random scattering of them, the effect of non-interference/interference remains.

Now, let's suppose that we have a particle source that fires particles of two different energies. For example, a red and a blue photon. (A blue photon has a shorter wavelength and more energy than its red cousin.)

  1. Does the dual nature of each particle appear as if two experiments were being conducted simultaneously? (i.e., two interference patterns)

  2. If the photons are of very different energy levels, will the size and spacing of the slits prevent the formation of one or the other interference pattern? Or, both? Or neither?

  3. Is there any mathematical relationship between two particles of different energies that will allow prediction of observed effects?

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Welcome to physics.stackexchange. The result of the experiment will be a superposition of two interference patterns. The zero orders of the blue and red patterns will coincide so it will look green. The higher orders do not coincide. The blue orders occur at roughly 20% smaller angles than the red.

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  • $\begingroup$ The shorter the wavelength the smaller the diffraction angle. Red would have a larger angle than blue. $\endgroup$ – Lambda Feb 2 at 15:21
  • $\begingroup$ Typo corrected @Lambda $\endgroup$ – my2cts Feb 2 at 15:54

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