FOUNDATIONS OF QUANTUM MECHANICS

104 CHAPTER IV. THE COPENHAGEN INTERPRETATION
IV. 5. 5
DOUBLE SLIT EXPERIMENT
Even more interesting is the famous interference experiment with the double slit. The wave function
corresponding to particles passing through the screen with the slits is, in analogy with (IV. 43),
ψ ds (q) =
{
1 √
2 a
if q ∈ [− A − a, − A + a] ∪ [A − a, A + a]
0 elsewhere
, (IV. 53)
where 2a is the width of each slit, 2A is the distance between the slits, and A ≫ a, see figure IV. 8.
2 A
2 a
|ψ ds (q)| 2
Figure IV. 8: The probability distribution in position for a double slit, 2 a is the width of each slit and
2 A the distance between the slits
The Fourier transform of this double square wave function ψ ds is
˜ψ ds (p) =
√
2 a
( Ap
) sin(ap/)
π cos . (IV. 54)
a p /
The function | ˜ψ ds | 2 again has the same form as the interference pattern for the slits on a photographic
plate placed far away, as can be seen in figure IV. 9.
2 π / a
2 π / A
| ˜ψ ds (p)| 2
Figure IV. 9: The interference pattern for the double slit