Originally Posted by

**philippeb8**
So we all know the double-slit experiment resulting in an interference pattern: either constructive or destructive, depending on the phase of the photon.

What if slit 1 receives photons of wavelength X and slit 2 receives photons of exactly wavelength X * 2.

Will there be any interference on the screen, wavelengths being exact factors of each other?

Unless the same wave/particle hits both slits, you won't get an interference pattern as all, even if the wavelengths match, because it's crucial to have the particles be in phase. Just moving the slits far enough apart (or somehow shielding them from each other) so that slit 1 only receives photons from source 1 while slit 2 only receives photons from source 2 will destroy the interference pattern, even if source 1 and 2 have the same wavelength (let alone if they have different wavelengths). Heck, even with a single source, if you set up the experiment such that each photon can definitely be said to go through one slit or the other unambiguously, you'll lose the interference pattern.

The interference is present specifically because a wave travels though both slits, and so can take different paths (with different lengths) to the same point on the detector, resulting in constructive or destructive interference.

Conserve energy. Commute with the Hamiltonian.