is there any exact solution to single electron (photon) double slit experiment?

Question

I mean exact model with exact formulas, that is obtained from quantum or classical optics that for examples describes fringe patterns as you know fringe patterns in single electron double slit experiment differs from Fraunhofer or Fresnel fringes.

Answer 1

Yes, if be exact you mean a formula that gives you a probability distribution of where the electron will hit the screen. The probability density is just the square of the wave function (or squared amplitude of the light wave if you look at it that way). So add the wave functions and then square them to calculate the interference patterns. The exact formulas, of course, depend on the exact geometry of your setup.

No, if by exact you mean a formula that tells you exactly where the electron hits the screen.

Answer 2

Even for calculation of intensity, expectation or probabiility functions at the image plane, there is no "exact model" for the single electron double-slit intereference because even the Schrodinger wave equation is still only an aprpoximation, as relativistic effects are not taken into consideration. Furthermore, the agreement between quantum interference and classical electromagnetic interference isn't exact either, because phase in EM theory has a spatial direction, while phase in quantum theory does not, leading to very slight differences in the way things come out after computation. The most precise current model of electron behavior is quantum electrodynamics, which is a field theory that has yielded excellent precision in prediction.

It is doubtful if any models in physics are "mathematically exact" representations of reality. At best, they are all approximations, even if some are highly accurate ones.

Answer 3

Read the end of the article here ---

http://en.wikipedia.org/wiki/Double-slit_experiment