Prediction of electron position

[username27]

Hi,
I am working on a problem where my goal is to predict the location of pedestrians with certain constraints. So I have equations for the pedestrian motion (using social forces model) which is based on the idea of pedestrians movements are based on the forces acting upon them. For example, if there is another pedestrian close by, the pedestrian will try to move away from him. That is pedestrian movement is based on the repulsion force acting upon him from other pedestrians.

I see this problem as a similar one from repulsion forces acting on electron clouds. So my question is,
let say there are two electron clouds at time k, and if you want to predict the location of the electron clouds at time (k+1), what equations are used? I am looking for the any useful links which shows how the distance and corresponding co-variance associated with the distance changes with time.

My background is not from physics, so please let me know if I am stating anything wrong.

 

[Chopin]

In quantum physics, the equation which governs this sort of calculation is the Schrödinger Equation. It allows you to compute the time evolution of a quantum wavefunction, subject to specified initial conditions and interaction forces.

However, if you are modeling the pedestrians as point particles (i.e. you are computing a definite position for each one), then you don't really need the formalism of quantum physics at all--you could just compute the problem classically. In that case, you would just use Newton's laws (F=ma) along with some suitable interaction force (electrodynamics and gravity both use force laws which are inversely proportional to the distance squared between the bodies, but you could choose something different for your application if it proves to work better). By using these equations, you will obtain a system of coupled differential equations, which you can solve numerically to map out the time evolution for each particle in the system.

 

[San K]

Statistical tools might be more useful than quantum, or classical, equations because:

The mind is making the calculations base on
environmental, psychological, social and cultural factors will play a role in "pedestrian replusion".

What are you trying to do, from a larger perspective?

 

[Jilang]

I don't think the Schrödinger equation will help you here. It is effectively a diffusion equation if you take out the i to make it classical. There is no assumed repulsive force as such and the particle density tends to spread out over time just as a drop of ink spreads out in a jar of water.

 

[vtahmoorian]

If you consider pedestrians probabilistically, it means you should use statistical mechanics ; so that you can predict a specific pedestrian's motion based on how often it feels others' forces and from which direction , since these factors are probabilistic , seems you need to take a look at " Langevin equation","Brownian motion" ,random walk" and modify them based on your scenario.

 

[username27]

By using these equations, you will obtain a system of coupled differential equations, which you can solve numerically to map out the time evolution for each particle in the system.

Thanks for the comment. But how do you find the uncertainty (variance) associated with the time of a particle based on solving the differential equations. That is where I have problems. All the approaches are giving the state of the target (x,y position) but not the uncertainty (variance) associated with those states.

 

[username27]

If you consider pedestrians probabilistically, it means you should use statistical mechanics ; so that you can predict a specific pedestrian's motion based on how often it feels others' forces and from which direction , since these factors are probabilistic , seems you need to take a look at " Langevin equation","Brownian motion" ,random walk" and modify them based on your scenario.

I have done the literature survey on that and finally ended with Social forces model, which suits for my requirement. So based on that I could able to determine state of a pedestrian (x,y location) but not the associated uncertainty (variance) with that state.

 

[username27]

What are you trying to do, from a larger perspective?

Prediction and tracking for pedestrians/any moving objects from measurement from a sensor. Constrain is, Moving objects motion is dependent on other moving objects in the area. So based on the literature survey, I found social forces model as a useful one. But it gives you the state (x, y position) not the uncertainty associated with that.

 

[Jilang]

You need to introduce a bit of random variability into it. So a pedestrian might or might not avoid another one depending on what he had for breakfast or how short signed he/she is. Otherwise the whole result will be completely determined by the equation you apply.