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Soliton-like Solutions To The Ordinary Schrödinger Equation Within Standard Quantum Mechanics
Full text linkIn recent times attention has been paid to the fact that (linear) wave equations admit of "soliton-like" solutions, known as localized waves or non-diffracting waves, which propagate without distortion in one direction. Such localized solutions (existing also for K-G or Dirac equations) are a priori suitable, more than gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, localized solutions exist even for the ordinary (linear) Schrödinger equation within standard quantum mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions (even if localized and "decaying") are not square-integrable, as well as plane or spherical waves: we show therefore how to obtain finite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. © 2012 American Institute of Physics.535Bateman, H., Courant, R., Hilbert, D., Stratton, J.A., (1941) Electromagnetic Theory, 2, p. 356. , (Cambridge University Press, Cambridge)(Wiley, New York), (McGraw-Hill, New York)Rached, M.Z., Recami, E., Figueroa, H.E., Rached, M.Z., Recami, E., Figueroa, H.E., Recami, E., Rached, M.Z., Localized waves: a review (2009) Adv. Imaging Electron Phys., 156, pp. 235-355. , 10.1140/epjd/e2002-00198-7, H. E. H. Figueroa, M. Z. Rached, E. Recami, 10.1016/S1076-5670(08)01404-3, See, e.g. e-print arXiv:physics/0109062;, references therein;, edited by and (Wiley, New York)Rached, M.Z., Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures (2006) J. Opt. Soc. Am. 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Cherenkov Radiation Versus X-shaped Localized Waves: Reply
No full textOur aim in this paper is a reply to Seshadri's comments [J. Opt. Soc. Am. A 29, 2532 (2012)] on a previous article of ours, titled "Cherenkov radiation versus X-shaped localized waves" [J. Opt. Soc. Am. A 27, 928 (2010)], as well as to his more extended criticism of the extended special relativity theory, called by him nonrestricted relativity, and in particular of the extended Maxwell equations. © 2012 Optical Society of America.291225362541Seshadri, S.R., Cherenkov radiation versus X-shaped localized waves: Comment (2012) J. Opt. Soc. Am. A, 29, pp. 2532-2535Zamboni-Rached, M., Recami, E., Besieris, I.M., Cherenkov radiation versus X-shaped localized waves (2010) J. Opt. Soc. Am. A, 27, pp. 928-934Walker, S.C., Kuperman, W.A., Cherenkov-Vavilov formulation of X waves (2007) Phys. Rev. Lett., 99, p. 244802Hernández-Figueroa, H.E., Zamboni-Rached, M., Recami, E., (2008) Localized Waves, Theory and Applications, , WileyLu, J.-Y., Greenleaf, J.F., Experimental verification of nondiffracting X-waves (1992) IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 39, pp. 441-446Saari, P., Reivelt, K., Evidence of X-shaped propagation invariant localized light waves (1997) Phys. Rev. Lett., 79, pp. 4135-4138Recami, E., Zamboni-Rached, M., Dartora, C.A., Localized X-shaped field generated by a superluminal charge (2004) Phys. Rev. e, 69, p. 027602. , and references thereinRecami, E., Zamboni-Rached, M., Localized waves: A review (2009) Adv. Imaging Electron Phys., 156, pp. 235-355Sommerfeld, A., Überlichtgeschwindigkeitsteilchen (1904) Proc. K. Ned. Akad. Wet., 8, pp. 346-367Sommerfeld, A., Zur electronentheorie (3 Tiele) (1905) Nach. Kgl. Ges. Wiss. Göttingen, Math. Naturwiss. Klasse 99-130, pp. 363-439. , 1904, 201-236Fröman, P.O., Historical background of the tachyon concept (1994) Arch. Hist. Exact Sci., 48, pp. 373-380Bilaniuk, O.-M., Deshpande, V.K., Sudarshan, E.C.G., Meta' relativity (1962) Am. J. Phys., 30, pp. 718-723Bilaniuk, O.-M., Sudarshan, E.C.G., Particles beyond the light barrier (1969) Phys. Today, 22, pp. 331-339Recami, E., Classical theory of tachyons (1986) Riv. Nuovo Cimento, 9 (6), pp. 1-178Mignani, R., Recami, E., Crossing relations derived from (extended) relativity (1975) Int. J. Theor. Phys., 12, pp. 299-320Pavšič, M., Recami, E., Charge conjugation and internal space-time symmetries (1982) Lett. Nuovo Cimento, 34, pp. 357-362Recami, E., Tachyon mechanics and causality: A systematic thorough analysis of the tachyon causal paradoxes (1987) Found. Phys., 17, pp. 239-296Barut, A.O., MacCarrone, G.D., Recami, E., On the shape of tachyons (1982) Nuovo Cimento A, 71, pp. 509-533Mignani, R., Recami, E., Tachyons do not emit Cherenkov radiation in vacuum (1973) Lett. Nuovo Cimento, 7, pp. 388-390Utkin, A.B., Droplet-shaped waves: Causal finite-support analogs of X-shaped waves (2012) J. Opt. Soc. Am. A, 29, pp. 457-462Morse, P.M., (1985) Theoretical Acoustics, , Princeton UniversityArias, E., Bessa, C.H.G., Svaiter, N.F., An analog fluid model for some tachyonic effects in Field Theory (2011) Mod. Phys. Lett. A 26, pp. 2335-2344. , and references thereinRecami, E., The Tolman antitelephone paradox: Its solution by tachyon mechanics 1985, reprinted in Electron (2009) J. Theor. Phys. (EJTP), 6, pp. 1-8Recami, E., Superluminal motions? A bird's-eye view of the experimental status-of-The-Art (2001) Found. Phys., 31, pp. 1119-1135Recami, E., Superluminal Waves and Objects: An Up-dated Overview of the Relevant Experiments, , arXiv :0804.1502 [physics]Recami, E., Rodrigues, W.A., A model theory for tachyons in two dimensions (1985) Gravitational Radiation and Relativity, 3, pp. 151-203. , J. Weber and T. M. Karade, eds., of Proceedings of the Sir Arthur Eddington Centenary Symposium World ScientificBarut, A.O., Chandola, H.C., Localized' tachyonic wavelet solutions to the wave equation (1993) Phys. Lett. A, 180, pp. 5-8Recami, E., Mignani, R., Magnetic monopoles and tachyons in special relativity (1976) Phys. Lett. B, 62, pp. 41-4
Erratum: Focused X-shaped Pulses (journal Of The Optical Society Of America A: Optics And Image Science, And Vision)
No full text[No abstract available]22122900Zamboni-Rached, M., Shaarawi, A.M., Recami, E., "Focused X-shaped pulses" (2004) J. Opt. Soc. Am. A, 21, pp. 1564-157
Radiation-induced fermion resonance
No full textThe Dirac equation is solved for two novel terms which describe the interaction energy between the half-integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation-induced fermion resonance
Elementary Particles As Micro-universes: A Geometric Approach To "strong Gravity"
No full textWe present here an overview of our unified, bi-scale theory of gravitational and strong interactions [which is mathematically analogous to the last version of N. Rosen's bi-metric theory, and yields physical results similar to those of strong gravity]. This theory, developed during the last 20 years, is purely geometrical in nature, adopting the methods of General Relativity for the description of hadron structure and strong interactions. In particular, hadrons are associated with "strong black holes", from the external point of view, and with "micro-universes", from the internal point of view. Results presented here include derivations of (i) confinement and (ii) asymptotic freedom for hadron constituents; (iii) Yukawa behaviour for the strong potential at the static limit; (iv) the strong coupling "constant", and (v) meson mass spectra.41716Ammiraju, P., Recami, E., Rodrigues, W.A., (1983) Nuovo Cimento A, 78, p. 172Ammiraju, P., (1991) Hadronic J., 14, p. 441Bekenstein, J.D., (1974) Phys. Rev. D, 9, p. 3292Broberg, H., (1987) Apeiron, 1, p. 6Broberg, H., (1993) Apeiron, 15, p. 10. , FebBrowne, P.F., (1994) Apeiron, 20, p. 6. , OctCaldirola, P., Pavsic, M., Recami, E., (1978) Nuovo Cimento B, 48, p. 205Caldirola, P., Pavsic, M., Recami, (1978) Phys. Lett. A, 66, p. 9Caldirola, P., Recami, E., (1979) Lett. Nuovo Cim., 24, p. 565Einstein, A., Do gravitational fields play an essential role in the structure of elementary particles? (1919) Sitzungsber. d. Preuss. Akad. d. Wiss. (in German)Hawking, S.W., (1975) Comm. Math. Phys., 43, p. 199Huber, P., (1982) Apeiron, 14, p. 15. , OctItaliano, A., Recami, E., (1984) Lett. Nuovo Cim., 40, p. 140Italiano, A., (1984) Hadronic J., 7, p. 1321Ivanenko, D.D., (1979) Astrofisica e Cosmologia, Gravitazione, Quanti e Relatività - Centenario di Einstein, p. 131. , edited by M. Pantaleo & F. de Finis (Giunti-BarberaFlorence)Jaakkola, T., (1987) Apeiron, 1, p. 5. , SepKokus, M., (1994) Apeiron, 20, p. 1. , OctMandelbrot, B.B., (1983) The Fractal Geometry of Nature, , W. H. FreemanSan FranciscoMarkov, M.A., (1966) Zh. Eksp. Teor. Fiz., 51, p. 878Mignani, R., (1976) Zh. Eksp. Teor. Fiz., 16, p. 6Oldershaw, R.L., (1986) Int. J. General Systems, 12, p. 137Pantaleo, M., (1955) Cinquant'anni di Relatività, , GiuntiFlorencePapapetrou, A., (1980), Private communicationPecker, J.-C., (1988) Apeiron, 2, p. 1. , FebPesteil, P., (1991) Apeiron, 11, p. 13. , AutQuigg, C., (1985) Report 85/126-T, , Fermilab, Sept. 1985Recami, E., (1979) Annuario '79, Enciclopedia EST-Mondadori, p. 59. , edited by E. Macorini (MondadoriMilan)Recami, E., (1982) Prog. Part. Nucl. Phys., 8, p. 401. , and refs. thereinRecami, E., (1983) Old and New Questions in Physics, Cosmology,..., , edited by A. van der Merwe (PlenumNew York)Recami, E., (1983) Found. Phys., 13, p. 341Recami, E., Castorina, P., (1976) Lett. Nuovo Cim., 15, p. 347Recami, E., Martínez, J.M., Zanchin, V.T., (1986) Prog. Part. Nucl. Phys., 17, p. 143Recami, E., Zanchin, V.T., (1982) Il Nuovo Saggiatore, 8 (2), p. 13Recami, E., Zanchin, V.T., (1986) Phys. Lett. B, 177, p. 304Phys. Lett. B, 181, pp. E416Recami, E., Zanchin, V.T., (1994) Found. Phys. Lett., 7, p. 85Recami, E., Zanchin, V.T., Vasconselos, M.T., (1995) Rev. Brasil. de Ensino de Física, 17, pp. 27-37Rosen, N., (1980) Found. Phys., 10, p. 673Sachs, M., (1981) Found. Phys., 11, p. 329Sachs, M., (1982) General Relativity and Matter, , ReidelDordrechtSalam, A., (1977) Ann. N. Y. Acad. Sci., 294, p. 12Salam, A., (1978) Proceed. 19th Int. Conf. High-Energy Physics (Tokyo, 1978), p. 937Salam, A., Strathdee, D., (1977) Phys. Rev. D, 16, p. 2668Salam, A., Strathdee, D., (1978) Phys. Rev. D, 18, p. 4596Sivaram, C., Sinha, K.P., (1979) Phys. Reports, 51, p. 111Zanchin, V.T., (1987), M.Sc. Thesis (UNICAMPCampinas, S.P.)Zanchin, V.T., Recami, E., Roversi, J.A., Brasca-Annes, L.A., (1994) Found. Phys. Lett., 7, p. 16
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