Double slit wavefunction

1. Dec 7, 2004

zeta101

Hi, just need a quick confirmation im 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!

Last edited: Dec 7, 2004
2. Dec 7, 2004

zeta101

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

TIA for any replies!

3. Dec 7, 2004

dextercioby

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.

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