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I am trying to do some simulations using the de Broglie - Bohm formalism and am wondering if there are computational tools that already exist in this area.

I generally use Python, but will consider anything, even if I have to put some numerical analysis theory into code.

That is, any theory or know-how in the forms of articles, websites or theses about implementing such tools is also welcome.

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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

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    $\begingroup$ It's not the same but I developed A program to simulate and calculate fringe patterns for various slit experiment. It's based on trajectories and you can change the wavelength and dimensions of the experiment. You can find my website billalsept.com at the top of my page. You'll find an article I wrote about this and the various slit simulators. $\endgroup$ – Bill Alsept Sep 13 '17 at 23:53
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    $\begingroup$ I'm voting to close this question as off-topic because it's about finding software and not physics. $\endgroup$ – Kyle Kanos Sep 14 '17 at 14:37
  • $\begingroup$ If you didn't notice, it is about finding a highly specific software used in a very narrow area of physics, as well as other resources. Where do you suggest I ask this question? $\endgroup$ – MadPhysicist Sep 14 '17 at 17:02
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    $\begingroup$ @KyleKanos what comes first the idea or the computation? Physics is the best area for the OP to ask this question because the members will better understand the problem and what needs to be calculated / simulated etc. $\endgroup$ – Bill Alsept Sep 14 '17 at 20:45
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    $\begingroup$ To give my 2 cents, I monitor Bohmian mechanics questions here and would never have seen this question on compsci (which from experience wouldn't have been able to give a satisfactory answer). Since the resource-recommendations tag exists this seems the best SE site to ask this question on; and given the specialist nature of BM, the only one likely to produce a relevant answer that'll also be useful to other people searching this topic in the future - I've noticed very few people on physics SE are even able to answer BM questions so I'm doubtful this question would ever get answered elsewhere. $\endgroup$ – Toby Hawkins Sep 14 '17 at 21:40
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I don't believe anyone's released any compiled tools or libraries specifically for Bohmian simulations, but for a few simple examples in Python using RK4, Dane Odekirk has an excellent git repository here. I'd start with reading the pdf there, then look at the code—it shouldn't be too hard to follow.

There are also several Mathematica examples here, and Marlon Metzger has created these neat animations in MATLAB/POV-Ray—you can find the code in the appendix of his bachelor's thesis (linked on the same page).

For a more in depth look at computational approaches to Bohmian calculations (if you want to do your own coding), 'Quantum Dynamics with Trajectories' by Robert Wyatt is a good resource—although like many academic books if you don't have access it's quite expensive (also if it matters it doesn't cover Python specifically, just general methods).

Paulo Machado's doctoral thesis (advised by Wyatt), 'Computational Approach to Bohm's Quantum Mechanics', might also be of interest, which contains some general methods—with MATLAB code in an appendix.

I believe the books 'A Trajectory Description of Quantum Processes. I. Fundamentals' and 'A Trajectory Description of Quantum Processes. II. Applications' by Sanz and Miret-Artez also cover similar methods.

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  • $\begingroup$ Much appreciated! I believe that Robert Wyatt's book will be of great help! $\endgroup$ – MadPhysicist Sep 14 '17 at 10:14
  • $\begingroup$ You're welcome. Yeah, I think that's probably a good starting point. You might also be interested that I've updated the answer with an additional free resource (Machado's thesis). $\endgroup$ – Toby Hawkins Sep 14 '17 at 13:58
  • $\begingroup$ I have looked through the intro of the book as well as the first couple of chapters, and it looks awesome! Not only is it a good resource for computational things, but it is also stellar on the Bohmian mechanics itself! Once again, much appreciated! $\endgroup$ – MadPhysicist Sep 14 '17 at 14:25
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Towler wrote about a simulation code named LOUIS in [1].

[1] M. D. Towler, N. J. Russell, and Antony Valentini. Time scales for dynamical relaxation to the born rule. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 468(2140):990–1013, 2012.

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