In the Copenhagen interpretation of quantum mechanics, a single photon or electron is described by a wave function that evolves over time. In the case of the double-slit experiment, the wave function of the particle initially spreads out like a wave, passing through both slits simultaneously. This wave-like behavior leads to an interference pattern on a screen placed behind the slits.
The distance between the slits in the double-slit experiment can indeed affect the outcome and the resulting interference pattern. The key factor is the wavelength of the particle or, equivalently, the de Broglie wavelength associated with the particle. The de Broglie wavelength is inversely proportional to the momentum of the particle and determines the spacing of the interference pattern.
When the distance between the slits is comparable to the de Broglie wavelength of the particle, the interference pattern will exhibit significant interference fringes. As the distance between the slits increases, the spacing between the interference fringes on the screen also increases. Conversely, if the distance between the slits is much larger than the de Broglie wavelength, the interference pattern becomes less pronounced, and the individual slit contributions become more prominent.
Therefore, the distance between the slits does play a role in determining the characteristics of the interference pattern observed in the double-slit experiment. It affects the spatial arrangement of the interference fringes and can influence the visibility and intensity of the resulting pattern.