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|the wave function on a given wave front, then we can express its value elsewhere as the sum of contributions from different elements of the wave front in the form of propagating spherical wave, e(2i r/)/r, where r is the distance from the point in question to the element of surface on the wave front, and is the wavelength. This spread of wave is somewhat similar to the pattern (in the wall behind) generated by firing a machine gun at an iron plate with two slits on it. Most of the bullets through the slits would align with each, some may be scattered sideways by hitting the edges although the chance becomes rarer as deviation getting further. One big difference is that bullets don't interfere with each other (story ascribed to Feynman). Anyway, assuming that the slit is very narrow, the two waves from slit 1 and 2 can be represented as:|
1 = Ae(2i r1/)/r1 ---------- (01a)
2 = Ae(2i r2/)/r2 ---------- (01b)
Figure 01 Double-slit Exp.
Figure 02 Probabilities [view large image]
|where A is the normalization constant, r1, and r2 are the distance from the slits to the screen as shown in Figure 01, which lays out the x-y plane only, while the z direction is perpendicular to the|