Single Slit Experiment: Details & Equations

[JordanGo]

Hello! I am looking for resources to give me details of the single slit experiment. I want to code a simulation of the experiment, but most information i find is too simple or missing details. I need equations for the two angles of the particle (angle with respect to x direction and angle with respect to y direction), also any other details that i may need, but it seems to be those angles that are of importance. And finally,
implementing wavefunctions so i can pick and choose particles and not just one.

Thanks!

 

[rumborak]

Hmm, I am not certain whether you know what the implementation entails.
As the "simplest" simulation you would implement a finite-grid wave equation ( http://en.wikipedia.org/wiki/Wave_equation ). That simulation would get you a realistic single-slit experiment.
But, you said "so i can pick and choose particles", which seems to indicate you rather want to implement a full quantum mechanics simulation. I have myself done the former (and even that is not the easiest thing to do), the latter is a totally different ballgame.

 

[sophiecentaur]

so i can pick and choose particles and not just one.

A single particle will not produce a diffraction pattern. It will turn up in one particular place. What do you actually want to achieve with this experiment. Are your trying to make a simulation?

 

[rumborak]

Err, single slit definitely produces interference patterns.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html

 

[sophiecentaur]

"Err" A single particle cannot produce a diffraction pattern. Of course, a single slit will produce a diffraction pattern when there are enough particles for the statistics to show it.
Note (from your reference, even) it is referred to as Diffraction and not Interference, which is the simple effect from multiple point sources.

 

[rumborak]

Oops, I apologize. :D

i think if he simulated the particles as wave packets, he would get the interference even with a single "particle" (particle here meant in this non-quantized sense), no?

 

[sophiecentaur]

What you get is a probability distribution. Same sums as for waves, in fact. But one particle will never form a diffraction pattern. Imo the difference is very relevant.
I think the OP is expecting to find something 'significant' in this simulation which is not really there. However, it could be an interesting programming exercise in translating the conventional Diffraction pattern values into random directions and building up a pattern over time.

 

[rumborak]

What you get is a probability distribution. Same sums as for waves, in fact. But one particle will never form a diffraction pattern. Imo the difference is very relevant.

Oh, absolutely, whether you treat the particle as a pure wave package (in which case you can simulate it easily with a regular wave equation) and get an interference pattern from a single "particle" that way, or whether you go the full route of simulating a quantized particle that exhibits particle/wave duality, makes a huge difference. I'm really only suggesting the "pure wave" approach to make the simulation more feasible.

I think the OP is expecting to find something 'significant' in this simulation which is not really there. However, it could be an interesting programming exercise in translating the conventional Diffraction pattern values into random directions and building up a pattern over time.

It's a very educational exercise indeed, but it's also not exactly something you whip up on an afternoon.

 

[sophiecentaur]

makes a huge difference.

I'm not sure what you are getting at here. The wave / particle duality idea is not something you can apply half and half, is it? Surely you have to choose one way or the other and do you not, then find the two results are the same?

but it's also not exactly something you whip up on an afternoon

I reckon you could do a 'near enough fudge' without too much trouble (even with Excel) that would look OK
But I wonder what the point of a simulation is, when the long terms result of the experiment is easy to work out very accurately.
Simulations worry me a lot and they seem to be getting more and more popular as Computer Games are used more and more.