Particles under two equal opposing forces

[Twelfthroot]

This question is probably either really easy or nonsensical, but I'm not versed in the physics involved.

Suppose we have a beam of positively charged particles firing along the y axis into a static planar electric field with strong negative charges on each side, such that at any point on the y axis the beam particles would experience two equal strong opposing forces summing to zero net force. Were the beam to deviate slightly, it would deflect strongly in the direction of deviation. We crank up the strength of the field as much as we can without observing any deflection in the beam. Now, we reduce beam until only one charged particle is emitted at a time.

Do we still observe that all of the particles went as straight as the original beam, or will quantum effects now ensure that we see a wider spread? In an ideal situation, would we observe a predictable distribution centered around the target point? In a practical situation? Would the width of the spread depend on the strength of the electric field? Are there other interesting phenomena we could observe in a setup like this, or am I just barking up an imaginary tree? Thanks in advance.

[gmalivuk]

I suspect we'd see diffusion right from the beginning, since the first time quantum effects show up is where we can't control the particles' momentum with complete precision, including direction.

[selfassembled]

I can only go with my intuition at this point but quantum self-interference should not come into play in this setup. That is, each one particle will fall somewhere randomly along the circular distribution outlined by the full beam. It is fundamentally different form the double slit experiment. Except...I just now considered the fact that a beam of positive particles would repel each other unless they were perfectly lined up...

Also, diffusion will most certainly be directly correlated to field strength and inversely correlated with beam velocity.

[eSOANEM]

This isn't a question of diffraction, it's a question of uncertainty. Excluding the situation where we have no knowledge of the particle's position, we must have some uncertainty in its momentum which includes uncertainty in direction of travel. Because of this, even a single particle will have some probability of deviating from the straight line path up the centre.