Double slit wavefunction

  • Thread starter zeta101
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  • #1
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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?

[tex]\Ket{\Psi} = C_1\Ket{\phi_1} + C_2\Ket{\phi_2}[/tex]

where [tex]\Ket{\phi_1}[/tex] and [tex]\Ket{\phi_2}[/tex] 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?

[tex]C_1 = 1/ |\Ket{\phi_1}|^2[/tex]

and etc for the other C?

Thanks!
 
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  • #2
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hmmm, my kets didnt come out, but still means the same thing!

TIA for any replies!
 
  • #3
dextercioby
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zeta101 said:
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 [itex] |\Psi>=C_{1}|\phi_{1}>+C_{2}|\phi_{2}> [/itex] 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 [itex] |\phi_{1}> [/itex] and [itex] |\phi_{2}> [/itex] ans use again the normalizations and the orthogonality between vectors.
 

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