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I want to model the 1D trajectory of an alpha particle post-emission. The alpha particle will be emitted in a cloud chamber and the particle will move over a coordinate plane that I will use to measure the distance that it traveled in the x-axis over time t. I will then use this information to solve for p by using: \begin{equation} t=\frac{L}{c}\sqrt{\frac{m^2c^2}{p^2}+1} \end{equation} I will use the momentum to determine the particles overall energy and then determine the classical Lagrangian equations of motion, which I will compare to a quantum prediction of the path by using the propagator.

Could this procedure work, or do I need another way to determine the momentum?

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  • $\begingroup$ Please have a look at our FAQ on writing question titles. $\endgroup$ – DanielSank Oct 19 '17 at 21:15
  • $\begingroup$ You lost me after "and then determine the classical Lagrangian equations…" but you have to be careful that the particle will loose enough energy/momentum as it propagates through the cloud chamber as to invalidate your equation. Moreover is your plan to use a high speed camera? Otherwise, I don't see how you would measure the timing… $\endgroup$ – user154997 Oct 19 '17 at 21:30
  • $\begingroup$ I was planning on using a high-speed camera to get precise timings. I'm confused by what you mean by, "you have to be careful that the particle will lose enough energy/momentum as it propagates through the cloud chamber as to invalidate your equation." Do I need to be concerned about the particle losing too much energy, or too little? Also, what specifically confuses you. I would love to add clarification, but I would like to know your specific misunderstanding. $\endgroup$ – Ethan Baker Oct 19 '17 at 21:40
  • $\begingroup$ Your equation assumes $p$ is constant but the particle will be stopped in the cloud chamber, no? So your equation is only valid for small enough segments of the track. But I guess you realised that after all. As for my other remark, it would have been more accurate to state that you did not give enough details for me to have a clear idea of what you want to do. $\endgroup$ – user154997 Oct 19 '17 at 22:01
  • $\begingroup$ a practical remark: when you answer a comment, it is best to include @name-of-the-person-whose-comment-you-answer, because then the said person gets a warming by the stackexchange interface. $\endgroup$ – user154997 Oct 19 '17 at 22:03
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Have a look at this video to see what the tracks look like coming from a source, or this from the ambient environment.

You can check the ionization formulae if you manage to find the velocity by using a fast camera.

This is a photo with tracks in a strong magnetic field perpendicular to the picture, which will help in the accuracy of determining p.

It gives an easier way to find the momentum from the radius using Bqv=mv^2/r and taking into account the ionisation loss.

alphamag

You seem to have a misunderstanding

then determine the classical Lagrangian equations of motion,

Suppose you have the momentum and know the ionisation loss, a straight line is the solution even if you use the whole aparatus of the lagrangian equations.

which I will compare to a quantum prediction of the path by using the propagator.

The only quantum prediction I can imagine on the path is the small scatters and ionization losses which have a quantum mechanical description. There is no quantum prediction for the origin of the track, other than the decay probability of the nucleus that gave rise to it, and that you cannot get from one track.

If you are thinking of wavepackets in quantum field theory, the width/thickness of the ionisation path is much larger than the size of the packet (estimated by using the heisenberg uncertainty)

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  • $\begingroup$ I now see the flaws in the “boringness” of the tracks. Would analyzing the path under the effect of a magnetic field be more interesting? That would also give me a more precise measure of momentum, as you point out of (which is also how they determine the momentum at ALICE). Also, do you suggest that I just abandon the QM approach, and just stick with the classical method, or is there a better QM approach. $\endgroup$ – Ethan Baker Oct 20 '17 at 10:07
  • $\begingroup$ As I said , I cannot see a quantum mechanical approach because on individual tracks or particles it it probabilistic. Only measured distributions are predicted by quantum mechanics, not trajectories. Quantum field theory makes wavepackets which with creation and annihilation operators model the propagation of a particle , but this is the same as the classical trajectory in a cloud chamber or bubble chamber. Our detectors are macroscopic per force ( unless we go to nanotechnology) $\endgroup$ – anna v Oct 20 '17 at 10:21
  • $\begingroup$ My interest in this project is seeing how the models compare. If they are the same that is fine for my purposes, it still provides me with valuable information. My real question is simply about the possibility of using the propagator to model the path. $\endgroup$ – Ethan Baker Oct 20 '17 at 11:10
  • $\begingroup$ Would this be more interesting by using background radiation instead of a source? The main issue I see with that is difficulty in finding initial conditions for the equations. $\endgroup$ – Ethan Baker Oct 21 '17 at 21:57
  • $\begingroup$ Do you have a link for this "propagator" of yours? $\endgroup$ – anna v Oct 22 '17 at 4:22

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