# Double slit experiment from first principles of QM

I have read many descriptions of electron double slit experiment but I could not find the description from the first principles of quantum mechanics. Most of the descriptions makes comparison with light waves or water waves and after some arguments from optics explain why the interference happens. Light waves and water wave description are not fundamental, they are phenomenological models. Could somebody explain the electron double slit interference only from the first principles of quantum mechanics? I know the answer from the Feynman path integral approach but I would like to understand it from the pre-Feynman Integral approach.

• Please make sure that I have read all the answers related to this question in the PSE. I am looking for a rigorous description of electron double slit interference patters only from the first principles of quantum mechanics (but not the Feynman Integral approach) Jul 9, 2014 at 13:46
• If you accept Schrodinger equation, you just have to consider infinite potential in the plan $z=0$ of the slits (except for the $2$ slits where the potential is zero); of course, you have to do numerical simulations. Jul 9, 2014 at 14:34
• Thank you for your insight but I have difficulty with performing the numerical simulations. It that the only way to explain it ? I am basically interested to understand why the two probability amplitudes due to the two slits are what they are? Basically the prepared states are definite momentum states along a direction perpendicular to the plane of the slits and the screen. What causes the probability amplitude to be identical with the prepared states? Jul 9, 2014 at 14:45
• " What causes the probability amplitude to be identical with the prepared states?" You must mean something else, as the amplitude is a number, not a state. Also, what about Feynman path integral disturbs you? It is from first principles, is it not? Just as some problems are hideously complicated in Newtonian mechanics but crystal clear in Lagrangian mechanics, so it can occur in QM that the path integral solves elegantly what is otherwise very ugly. Jul 9, 2014 at 16:47
• Dear ACuriousMind, What I am interested to know is how to establish the probability amplitude of the expressions in the Copenhagen interpretation. The probability amplitude from the two slits are only different in phase but have the same wave number. I could not understand how does that happen? I am asking this question to understand the Copenhagen interpretation in relation to the double slit experiment. Jul 9, 2014 at 18:58