Artículo

La versión final de este artículo es de uso interno. El editor solo permite incluir en el repositorio el artículo en su versión post-print. Por favor, si usted la posee enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

A mathematical formalism that allows to deal with many problems on quantum systems with continuous evolution spectrum is presented. The usual Hilbert space is generalized to a prehilbert one T where singular states can be represented and an extended Dirac's notation can be introduced. The obtained formalism contains the Van Hove one but in a more natural way. It allows to explain decoherence and other phenomena. © 2007 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum
Autor:Murgida, G.; Castagnino, M.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Continuous spectrum; Normalization; Van Hove's formalism; Eigenvalues and eigenfunctions; Hilbert spaces; Problem solving; Quantum theory; Spectrum analysis; Continuous spectrum; Evolution spectrum; Normalization; Quantum systems; Van Hove's formalism; Hamiltonians
Año:2007
Volumen:381
Número:1-2
Página de inicio:170
Página de fin:188
DOI: http://dx.doi.org/10.1016/j.physa.2007.03.035
Título revista:Physica A: Statistical Mechanics and its Applications
Título revista abreviado:Phys A Stat Mech Appl
ISSN:03784371
CODEN:PHYAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v381_n1-2_p170_Murgida

Referencias:

  • Laura, R., Castagnino, M., (1998) Phys. Rev. A, 57, p. 4140
  • Laura, R., Castagnino, M., (1998) Phys. Rev. E, 57, p. 3948
  • Castagnino, M., Laura, R., Liotta, R., Id Betan, R., (2002) J. Phys. A, 35, p. 6055
  • Castagnino, M., Laura, R., (2000) Phys. Rev. A, 62, p. 22107
  • Castagnino, M., (2004) Physica A, 335, p. 511
  • Castagnino, M., Laura, R., (2000) Int. J. Theor. Phys., 39, p. 1767
  • Castagnino, M., Lombardi, O., (2003) Int. J. Theor. Phys., 42, p. 1281
  • Castagnino, M., (2005) Braz. J. Phys., 35, p. 375
  • Castagnino, M., Lombardi, O., (2006) Chaos, Solitons Fractals, 28, p. 879
  • Castagnino, M., Ordoñez, A., (2004) Int. J. Theor. Phys., 43, p. 695
  • Castagnino, M., Lombardi, O., (2005) Phys. Rev. A, 72, p. 012102
  • Cotlar, M., (1968) Equipación con Espacios de Hilbert, , Universidad de Buenos Aires, Buenos Aires
  • Balentine, L., (1990) Quantum Mechanics, , Prentice-Hall, New Jersey
  • Gelfand, I.M., Vilekin, N., (1964) Generalized Functions, 4. , Academic Press, New York
  • Castagnino, M., Laura, R., (1997) Phys. Rev. A, 56, p. 108
  • Antoniou, I., Suchanecki, Z., Laura, R., Tasaki, S., (1997) Physica A, 241, p. 737
  • Segal, I.E., Postulates for quantum general quantum mechanics (1947) Ann. Math., 48 (4), p. 930
  • Antoniou, I., Suchanecki, Z., (1995) Nonlinear, Deformed and Irreversible Quantum Systems, , World Scientific, Singapore
  • Van Hove, L., (1955) Physica, 21, p. 901
  • Van Hove, L., (1956) Physica, 22, p. 343
  • Van Hove, L., (1959) Physica, 25, p. 268
  • Fava, N., Zo, F., (1996) Medida e Integral de Lebesgue, , Red Olimpica, Buenos Aires
  • van Kampen, N.G., (1954) Physica, 20, p. 603
  • Daneri, A., Loinger, A., Prosperi, G., (1962) Nucl. Phys., 33, p. 297
  • Segal, I., (1969) Bull. Am. Math. Soc., 75, p. 1390
  • Zurek, W.H., (1981) Phys. Rev. D, 24, p. 1516
  • Zurek, W.H., (1991) Phys. Today, 44, p. 36
  • Zurek, W.H., (2003) Rev. Mod. Phys., 75, p. 715
  • Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J., Stamatescu, I.-O., (2003) Decoherence and the Appearance of a Classical World in Quantum Theory, , Springer, Heidelberg
  • Knill, E., Laflamme, R., Barnum, H., Dalvit, D., Dziarmaga, J., Gubernatis, J., Gurvits, L., Zurek, W.H., (2002) Los Alamos Sci., 27, p. 2
  • Casati, G., Chirikov, B., (1995) Phys. Rev. Lett., 75, p. 349
  • Casati, G., Chirikov, B., (1995) Physica D, 86, p. 220
  • Penrose, R., (1995) Shadows of the Mind, , Oxford University Press, Oxford
  • Diósi, L., (1987) Phys. Lett. A, 120, p. 377
  • Diósi, L., (1989) Phys. Rev. A, 40, p. 1165
  • Milburn, G.J., (1991) Phys. Rev. A, 44, p. 5401
  • Adler, S., (2004) Quantum Theory as an Emergent Phenomenon, , Cambridge University Press, Cambridge
  • Castagnino, M., Gadella, M., Laura, R., Id Betan, R., (2001) Phys. Lett. A, 282, p. 245
  • Castagnino, M., Gadella, M., Laura, R., Id Betan, R., (2001) J. Phys. A, 34, p. 10067
  • Castagnino, M., Lombardi, O., (2004) Stud. Hist. Philos. Mod. Phys., 35, p. 73
  • Castagnino, M., Lombardi, O., (2005) Philos. Sci., 72, p. 764

Citas:

---------- APA ----------
Murgida, G. & Castagnino, M. (2007) . A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum. Physica A: Statistical Mechanics and its Applications, 381(1-2), 170-188.
http://dx.doi.org/10.1016/j.physa.2007.03.035
---------- CHICAGO ----------
Murgida, G., Castagnino, M. "A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum" . Physica A: Statistical Mechanics and its Applications 381, no. 1-2 (2007) : 170-188.
http://dx.doi.org/10.1016/j.physa.2007.03.035
---------- MLA ----------
Murgida, G., Castagnino, M. "A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum" . Physica A: Statistical Mechanics and its Applications, vol. 381, no. 1-2, 2007, pp. 170-188.
http://dx.doi.org/10.1016/j.physa.2007.03.035
---------- VANCOUVER ----------
Murgida, G., Castagnino, M. A natural normalization for the eigenstates of a Hamiltonian with continuous spectrum. Phys A Stat Mech Appl. 2007;381(1-2):170-188.
http://dx.doi.org/10.1016/j.physa.2007.03.035