How is the wavefunction defined in the double slit experiment for electrons?

[zeta101]

Hi, just need a quick confirmation I am right with something! :)

If we are considering electrons (for example) going through the double slit experiment one at a time would it be correct to define the wavefunction for the electron as follows?

$$\Ket{\Psi} = C_1\Ket{\phi_1} + C_2\Ket{\phi_2}$$

where $$\Ket{\phi_1}$$ and $$\Ket{\phi_2}$$ are eigenfunctions representing the electron going trhough slit 1 or slit 2 respectively and the C's are just some constants.

Actually, about the C's, would they be defined as follows?

$$C_1 = 1/ |\Ket{\phi_1}|^2$$

and etc for the other C?

Thanks!

 

[zeta101]

hmmm, my kets didnt come out, but still means the same thing!

TIA for any replies!

 

[dextercioby]

hmmm, my kets didnt come out, but still means the same thing!

TIA for any replies!

Yes,quantum phenomenology requires that the state vector of the system be written as a linear combination of vectors for the each slit (event) which are themselves normed and we have reasons to believe to mutual ortogonal.
Write $|\Psi>=C_{1}|\phi_{1}>+C_{2}|\phi_{2}>$ and then use Dirac trick apply the corresponding "bra" .Use normalization for each vector and u can come up with the interpretation of those constants in terms of probabilities.
For the expression of each constant,apply 2 times the 2 "bra"s corresponding to $|\phi_{1}>$ and $|\phi_{2}>$ ans use again the normalizations and the orthogonality between vectors.