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I am an undergraudate physics and math major. For context, I've taken senior level quantum 1 as well as real and complex analysis. I'd be really interested in focusing on understanding the mathematical formulation of Bohemian mechanics for a research project in my quantum mechanics 2 class but I can't seem to find any good introductory resources on the topic.

Any help would be appreciated!

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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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The best starting point, I think, is reading Bohm's first two papers on it (especially the first one which covers where the Bohmian quantum potential comes from):

A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I

A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

If you'd also like some historical context the book, Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference, is excellent.

Beyond that there are plenty of resources listed here www.bohmian-mechanics.net.

If you're looking for something more specific, let me know and I'll modify this answer.

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I highly recommend the book "Bohmian mechanics" by Stefan Teufel and Detlef Dürr.

It is written as an introductory book in the topic but also contains, in the later chapters, some details for the reader who is more deeply interested, also in the mathematical formulation. The original papers of Bohm are now quite old and the formulation given by Dürr et. al. that can be read up in the mentioned book is much easier to understand.

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There is a grand distinction between the formalism of de Broglie and Bohm, and what wrote their followers. These followers do not exactly agree among themselves on different issues, very important. So, before reading texts of the followers of de Broglie and Bohm, one should read BOHM's OWN ARTICLES

David Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables”, I and II., Phys. Rev. 85, pages 166-179, 180-193, (1952).

Now, for whoever wants to embarque on investigation of Bohm's mechanics, I have to say a couple of facts:

  1. Bohm's mechanics is not relativistic. Many efforts were done to solve this problems, but in vain. I don't want to write an explanation here, because it would be long, but if somebody needs help, I am ready to answer to a message.
  2. Bohm's mechanics doesn't succeed to include the photon. While for particles possessing rest-mass it gives a formalism based on the concepts of "particles" and "continuous trajectories", photons don't fit into this formalism. They don't have particles following continuous trajectories.
  3. Worse than that, some followers of Bohm claim that all the bosons cannot have particles following continuous trajectories.
  4. There are debates about the compatibility of Bohm's mechanics with the experiment, EVEN for particles possessing rest-mass: one debate was around the experiment proposed by Partha Ghose and performed by Brida; another debate not solved until today and of much bigger proportion, was triggered by the so-called "ESSW experiment" (B-G. Englert, M. O. Scully, G. Süssmann, H. Walther, “Surrealistic Bohm Trajectories”, Z. Naturforsch. 47a, 1175, (1992)).
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  • $\begingroup$ The question was surely not asking for prejudiced criticism of the theory, but for resources covering it. $\endgroup$ – Luke Sep 25 '18 at 11:25
  • $\begingroup$ @Luke Do you have any idea of what you write? Are you trying to educate people what to recommend? Mr. "mentor", to your knowledge, resources about Bohm's mechanics are, some positive, and some negative. To your knowledge, when one is before a court of law, one is required to say the truth, ONLY the truth, and ALL the truth. $\endgroup$ – Sofia Sep 27 '18 at 18:49
  • $\begingroup$ @Luke Do you understand what you write? Are you trying to educate people what to recommend? Mr. "mentor", resources about Bohm's mechanics are, some positive, some negative. One who embarqes on studying a theory has to know the criticism on it, for making his decision if he trusts or not the theory, and if he is willing to invest in it YEARS OF HIS LIFE. Do you understand what is YEARS OF LIFE, Mr. "mentor"? By the way, before a court of law, one is required to say the truth, ONLY the truth, and ALL the truth. As to Dürr's book it's not Bohm's mechanics, it's Dürr's understanding of it. $\endgroup$ – Sofia Sep 27 '18 at 19:09
  • $\begingroup$ @Luke Please don't bother yourself to reply to me, I am extremely busy. If somebody asks my opinion, I may answer, if I have time, but THAT'S ALL! I have no time for arguing. Bohm's mecanics is not valid for photons, not valid for relativism, the Bohmian trajectories are VERY contradictory. This is the truth. Good bye! $\endgroup$ – Sofia Sep 27 '18 at 19:19

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