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A new nonlinear Schrodinger equation

  1. Nov 19, 2005 #1
    At this link:
    http://www.geocities.com/ptep_online/PP-04-07.PDF
    is a recent paper by Carlos Castro on a new nonlinear Schrodinger equation--for those that work in this area.
     
  2. jcsd
  3. Nov 20, 2005 #2
    I have red your paper and, if you give me the permission, I shall give you now my sensations about it.
    1) Firstly, I got a surprise with the datum: January 2006, because we are in November 2005;
    2) It seems to be a new review of physics because it is volume 1 and there is no page. These two first points are acting on me like a warning signal: what is this? Where does it come from? Certainly a quantum experiment (smile), I mean a work coming from the future … (smile)
    3) The idea of fractal trajectories is (at least in my mind) a great one because it could be an elegant way of reconciliation between a classical and a quantum point of view; and (personal remark) is in someway what I am personally working about when I speak from photons springing from a piece of geodesic to another one (etgb28.pdf); the only point was: I didn’t knew that I was dealing with fractal trajectories as Mister Jourdain in Molières work (French writer in the 1700…) didn’t knew that he was doing “prose” when he was writing and speaking.
    4) I remark that the Schrödinger equation is obtained with a classical formulation of the Newton’s Law (which is avoiding a relativistic approach before any calculation has been done) if one considers the left part of equation (7) page 2, but with a special (due to Nottale) formulation of the acceleration if one observes the middle part of the same equation; so, it is not really the classical Newton’s Law but an extension of it including a “complex-time” derivative operator (page 2 relation3). Why not?
    5) One point is not clear for me; does the introduction of a complex number D (instead of the use of a real one at the beginning of the article) allows an extension of the work of Nottale and all to non-flat universe?
    6) One other point is not clear: is not the middle term page 6 in (40 on the left hand) and in (42; the integrand) equal to zero if the particle-wave following a geodesic (as required by GR in a 4D space)?
    Thank you for explanations.
     
  4. Nov 20, 2005 #3
    Yes, I should have also included this link to the journal table of contents. http://www.geocities.com/ptep_online/2006.html
    This is an "online" journal, thus papers are submitted and approved ahead of time of final publish, not uncommon in this age of internet access to journals.
    As to your detailed questions on the physics, I have no answers, you would need to contact the prime author, Dr. Castro--there is an email address on the paper.
     
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