Interference pattern calculations for unequal slits per QM theory

[San K]

I am trying to understand how QM theory (wave-functions) are applied to Interference pattern calculations for unequal slits for a single particle double slit experiment

case 1: both slits are equidistant from the "center", however one slit is bigger and the ratio of the width between the slits is say 80:20

case 1: equidistant but different slit width

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case 2: both the slits are equal width however one slit is father away from the slit than the other and the ratio of the distances from the center is in the ratio of say 80:20

case 2: same width of slits but not equidistant

how would we go calculating/prediction the interference pattern per QM (wave-function)?

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for case 1:

would we assume (per QM theory) that 20% of the wave function passes through the narrower slit and 80% of the wave-function passed through the wider slit? ...and then interferes?

for case 2:

what do we have to assume for the wave-function?

 

[Bill_K]

Would you be able to calculate the interference pattern if it were some other kind of wave? Sound waves, or light waves? All such problems have a common approach: Huyghens principle.

For each possible path calculate the amplitude and phase, then add them all up.

 

[San K]

Would you be able to calculate the interference pattern if it were some other kind of wave? Sound waves, or light waves? All such problems have a common approach: Huyghens principle.

For each possible path calculate the amplitude and phase, then add them all up.

thanks Bill K. i was not aware of the Hyugens–Fresnel principle, however thanks for putting me on the right track.

 

[azdavesoul]

I just acquired a new (to me) HENE laser and tried to create the pattern as described in Case 1. IMG_0096.JPG is a normal double slit, .35mm center with two .15mm slits. For image IMG_0097.JPG, I changed the slits to .1mm on the left and .4mm on the right. I will try to get better images when I have the time but there does seem to be a difference between the two sides.

 

[San K]

I just acquired a new (to me) HENE laser and tried to create the pattern as described in Case 1. IMG_0096.JPG is a normal double slit, .35mm center with two .15mm slits. For image IMG_0097.JPG, I changed the slits to .1mm on the left and .4mm on the right. I will try to get better images when I have the time but there does seem to be a difference between the two sides.

nice pics azdavesoul, great experiment

 

[azdavesoul]

San K,
You may be interested in some of the other diffraction patterns on my site, asymmetricphotons.com.

http://asymmetricphotons.davehewitt.com/__oneclick_uploads/2012/03/asymm.JPG