Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation

Nonadiabatic effects in the nuclear dynamics of the H 2 + molecular ion, initiated by ionization of the H 2 molecule, is studied by means of the probability and flux distribution functions arising from the space fractional Schrödinger equation. In order to solve the fractional Schrödinger eigenvalue...

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2019
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Universidad de Medellín
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Repositorio UDEM
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eng
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oai:repository.udem.edu.co:11407/6096
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http://hdl.handle.net/11407/6096
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oai_identifier_str oai:repository.udem.edu.co:11407/6096
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.none.fl_str_mv Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
spellingShingle Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title_short Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title_full Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title_fullStr Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title_full_unstemmed Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
title_sort Nonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equation
description Nonadiabatic effects in the nuclear dynamics of the H 2 + molecular ion, initiated by ionization of the H 2 molecule, is studied by means of the probability and flux distribution functions arising from the space fractional Schrödinger equation. In order to solve the fractional Schrödinger eigenvalue equation, it is shown that the quantum Riesz fractional derivative operator fulfills the usual properties of the quantum momentum operator acting on the bra and ket vectors of the abstract Hilbert space. Then, the fractional Fourier grid Hamiltonian method is implemented and applied to molecular vibrations. The eigenenergies and eigenfunctions of the fractional Schrödinger equation describing the vibrational motion of the H 2 + and D 2 + molecules are analyzed. In particular, it is shown that the position-momentum Heisenberg's uncertainty relationship holds independently of the fractional Schrödinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schrödinger equation for taking into account nonadiabatic effects. © 2019 Wiley Periodicals, Inc.
publishDate 2019
dc.date.accessioned.none.fl_str_mv 2021-02-05T14:59:35Z
dc.date.available.none.fl_str_mv 2021-02-05T14:59:35Z
dc.date.none.fl_str_mv 2019
dc.type.eng.fl_str_mv Article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.issn.none.fl_str_mv 207608
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/6096
dc.identifier.doi.none.fl_str_mv 10.1002/qua.25952
identifier_str_mv 207608
10.1002/qua.25952
url http://hdl.handle.net/11407/6096
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.references.none.fl_str_mv Landau, L.D., (1932) Phys Z Sowjetunion, 2, p. 46
Zener, C., (1932) Proc R Soc London A, 137, p. 696
Tully, J.C., (2012) J Chem Phys, 137, p. 22A301
Diestler, D.J., Manz, J., Pérez-Torres, J.F., (2018) Chem Phys, 514, p. 67
Pérez-Torres, J.F., (2013) Phys Rev A, 87, p. 062512
Hermann, G., PAulus, B., Pérez-Torres, J.F., Pohl, V., (2014) Phys Rev A, 89, p. 052504
Laskin, N., (2000) Phys Rev E, 62, p. 3135
Riesz, M., (1949) Acta Math, 81, p. 1
Laskin, N., (2002) Phys Rev E, 66. , 056108
Lenzi, E.K., Oliveira, B.F., Astrath, N.G.C., Malacarne, L.C., Mendes, R.S., Baesso, M.L., (2008) Eur Phys J B, 62, p. 155
Stickler, B.A., (2013) Phys Rev E, 88. , 012120
Longhi, S., (2015) Opt Lett, 40, p. 1117
Zhang, Y., Liu, X., Belić, M.R., Zhong, W., Zhang, Y., Xiao, M., (2015) Phys Rev Lett, 115. , 180403
Hermann, R., (2013) Int J Mod Phys B, 27. , 1350019
Dong, J., Xu, M., (2007) J Math Phys, 48. , 072105
Amore, P., Fernández, F.M., Hofmann, C.P., Sáenz, R., (2010) J Math Phys, 51. , 122101
Bhrawy, A.H., Abdelkawy, M.A., (2015) J Comput Phys, 294, p. 462
Bhrawy, A.H., Zaky, M.A., (2017) Appl Num Math, 111, p. 197
Marston, C.C., Balint-Kurti, G.G., (1989) J Chem Phys, 91, p. 3571
Tannor, D.J., (2007) Introduction to Quantum Mechanics, A Time-Dependent Perspective, , University Science Books, Sausalito, California
Layton, E., Chu, S.I., (1991) Chem Phys Lett, 186, p. 100
Yao, G., Chu, S.I., (1992) Phys Rev A, 45, p. 6735
Brau, F., Semay, C., (1998) J of Comp Phys, 139, p. 127
Stare, J., Balint-Kurti, G.G., (2003) J Phys Chem A, 107, p. 7204
Sarkar, P., Ahamed, B., (2011) Int J Quantum Chem, 111, p. 2268
Wei, Y., (2015) Int J Theor Math Phys, 5. , 58
Dirac, P.A.M., (1939) Math Proc Cambridge Philos Soc, 35, p. 416
Dirac, P.A.M., (1958) The Principles of Quantum Mechanics, , 4th, ed.,, Clareondon, Oxford
Karr, J.P., Hilico, L., (2006) J Phys B: At Mol Opt Phys, 39, p. 2095
Epstein, S.T., (1966) J Chem Phys, 44, p. 836
http:physics.nist.gov/cuu/Constants, CODATA international recommended values of the fundamental physical constants;, (accessed March 2019)
Wei, Y., (2016) Phys Rev E, 93, p. 066103
Schrödinger, E., (1926) Ann Phys (Leipzig), 81, p. 109
Manz, J., Pérez-Torres, J.F., Yang, Y., (2013) Phys Rev Lett, 111. , 153004
Albert, J., Hader, K., Engel, V., (2017) J Chem Phys, 147. , 241101
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.none.fl_str_mv John Wiley and Sons Inc.
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
publisher.none.fl_str_mv John Wiley and Sons Inc.
dc.source.none.fl_str_mv International Journal of Quantum Chemistry
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 20192021-02-05T14:59:35Z2021-02-05T14:59:35Z207608http://hdl.handle.net/11407/609610.1002/qua.25952Nonadiabatic effects in the nuclear dynamics of the H 2 + molecular ion, initiated by ionization of the H 2 molecule, is studied by means of the probability and flux distribution functions arising from the space fractional Schrödinger equation. In order to solve the fractional Schrödinger eigenvalue equation, it is shown that the quantum Riesz fractional derivative operator fulfills the usual properties of the quantum momentum operator acting on the bra and ket vectors of the abstract Hilbert space. Then, the fractional Fourier grid Hamiltonian method is implemented and applied to molecular vibrations. The eigenenergies and eigenfunctions of the fractional Schrödinger equation describing the vibrational motion of the H 2 + and D 2 + molecules are analyzed. In particular, it is shown that the position-momentum Heisenberg's uncertainty relationship holds independently of the fractional Schrödinger equation. Finally, the probability and flux distributions are presented, demonstrating the applicability of the fractional Schrödinger equation for taking into account nonadiabatic effects. © 2019 Wiley Periodicals, Inc.engJohn Wiley and Sons Inc.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85064484900&doi=10.1002%2fqua.25952&partnerID=40&md5=5de1c1ba9780c5a24817aa5427682249Landau, L.D., (1932) Phys Z Sowjetunion, 2, p. 46Zener, C., (1932) Proc R Soc London A, 137, p. 696Tully, J.C., (2012) J Chem Phys, 137, p. 22A301Diestler, D.J., Manz, J., Pérez-Torres, J.F., (2018) Chem Phys, 514, p. 67Pérez-Torres, J.F., (2013) Phys Rev A, 87, p. 062512Hermann, G., PAulus, B., Pérez-Torres, J.F., Pohl, V., (2014) Phys Rev A, 89, p. 052504Laskin, N., (2000) Phys Rev E, 62, p. 3135Riesz, M., (1949) Acta Math, 81, p. 1Laskin, N., (2002) Phys Rev E, 66. , 056108Lenzi, E.K., Oliveira, B.F., Astrath, N.G.C., Malacarne, L.C., Mendes, R.S., Baesso, M.L., (2008) Eur Phys J B, 62, p. 155Stickler, B.A., (2013) Phys Rev E, 88. , 012120Longhi, S., (2015) Opt Lett, 40, p. 1117Zhang, Y., Liu, X., Belić, M.R., Zhong, W., Zhang, Y., Xiao, M., (2015) Phys Rev Lett, 115. , 180403Hermann, R., (2013) Int J Mod Phys B, 27. , 1350019Dong, J., Xu, M., (2007) J Math Phys, 48. , 072105Amore, P., Fernández, F.M., Hofmann, C.P., Sáenz, R., (2010) J Math Phys, 51. , 122101Bhrawy, A.H., Abdelkawy, M.A., (2015) J Comput Phys, 294, p. 462Bhrawy, A.H., Zaky, M.A., (2017) Appl Num Math, 111, p. 197Marston, C.C., Balint-Kurti, G.G., (1989) J Chem Phys, 91, p. 3571Tannor, D.J., (2007) Introduction to Quantum Mechanics, A Time-Dependent Perspective, , University Science Books, Sausalito, CaliforniaLayton, E., Chu, S.I., (1991) Chem Phys Lett, 186, p. 100Yao, G., Chu, S.I., (1992) Phys Rev A, 45, p. 6735Brau, F., Semay, C., (1998) J of Comp Phys, 139, p. 127Stare, J., Balint-Kurti, G.G., (2003) J Phys Chem A, 107, p. 7204Sarkar, P., Ahamed, B., (2011) Int J Quantum Chem, 111, p. 2268Wei, Y., (2015) Int J Theor Math Phys, 5. , 58Dirac, P.A.M., (1939) Math Proc Cambridge Philos Soc, 35, p. 416Dirac, P.A.M., (1958) The Principles of Quantum Mechanics, , 4th, ed.,, Clareondon, OxfordKarr, J.P., Hilico, L., (2006) J Phys B: At Mol Opt Phys, 39, p. 2095Epstein, S.T., (1966) J Chem Phys, 44, p. 836http:physics.nist.gov/cuu/Constants, CODATA international recommended values of the fundamental physical constants;, (accessed March 2019)Wei, Y., (2016) Phys Rev E, 93, p. 066103Schrödinger, E., (1926) Ann Phys (Leipzig), 81, p. 109Manz, J., Pérez-Torres, J.F., Yang, Y., (2013) Phys Rev Lett, 111. , 153004Albert, J., Hader, K., Engel, V., (2017) J Chem Phys, 147. , 241101International Journal of Quantum ChemistryNonadiabatic effects in the nuclear probability and flux densities through the fractional Schrödinger equationArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Medina, L.Y., Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaNúñez-Zarur, F., Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaPérez-Torres, J.F., Escuela de Química, Universidad Industrial de Santander, Bucaramanga, Colombiahttp://purl.org/coar/access_right/c_16ecMedina L.Y.Núñez-Zarur F.Pérez-Torres J.F.11407/6096oai:repository.udem.edu.co:11407/60962021-02-05 09:59:35.451Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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