the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits.
an electron starts out with a wave function that is clustered near the point of emission and then evolves on some way according to the Shroedinger equation. What is this wave function? How does the slitted barrier modify say a wave function that would otherwise have been Gaussian?
malawi_glenn
Sep30-08, 09:18 AM
It is hard to give you a specific answer since you are asking what kind of wave function is entering the double slit; it depends on what situation you have I would say. It could be a plane wave, spherical wave etc.
Assuing the double slit is beeing illuminated by a current of particles with plane waves, the distortion of this wave "is done" in the same way as with classical waves. The non relativistic quantum mechanics formalism is basically wave physics mixed with probability theory (and other stuff such as Functional analysis etc)
wofsy
Sep30-08, 10:26 AM
Glenn
thanks so much for your help.
I guess the source of my questions was this underlying idea that there are only two things that happen in QM, solutions to the SE and measurements.
Solutions to the SE are solutions of linear equation and so can not explain measurements.
On the other hand there are superficially non-linear events such as collisions which can not possibly be solutions of the SE and I was trying to see what really happens so that the SE is obeyed.
The double slit seems related to this because if there is no slit then there is a barrier that prevents the electron from passing through to the detecting screen so this barrier must affect the wave function/interact with the electron somehow. With a single slit the barrier must still be at work except now it has an escape hole. The mathematics of this situation is what I was after since the SE is the only thing at work.
Again, thanks for your help.
ZapperZ
Sep30-08, 10:48 AM
the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits.
Does it really? Read the Marcella paper:
T.V. Marcella Eur. J. Phys. v.23, p.615 (2002). The preprint can be obtained here (http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf).