Skip to main content
Erschienen in: Journal of Nanoparticle Research 7/2020

01.07.2020 | Research paper

Behavior of an electron in the vicinity of a tridimensional charged polar nanoparticle through a classical and quantum constant of motion

verfasst von: Alejandro Castellanos-Jaramillo, Sergio Gutiérrez-López, Arnulfo Castellanos-Moreno

Erschienen in: Journal of Nanoparticle Research | Ausgabe 7/2020

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We present a classical and a quantum constant of motion used to study the behavior of an electron moving in the vicinity of a tridimensional charged nanostructure with electric dipole. It is the generalization of the bidimensional version studied in a previous work. The classical case is found by using two approaches: the Hamilton Jacobi equation and a Newtonian treatment. The quantum case is obtained by separating the Schrödinger equation in spherical coordinates. We use three quantum numbers to classify the states. The angular part is solved by using an expansion of spherical harmonics to get an eigenvalue equation for the new constant of motion. The solution shows that the probability density of the electron shifts toward the values where \(\theta <\frac {\pi }{2}\). The eigenvalue λ is near the value l(l + 1) of the angular momentum, but their difference grows if the electric dipole increases, so that the effect is small for a cluster like (GaAs)3 but very important for fullerenes like RbC60 and LiC60. The radial part is solved using the shooting method and we find the ground state, and first and second excited states.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Antoine R, Rayane D, Benichou E, Dugourd P h, Broyer M (2000) Electric dipole moment and charge transfer in alkali-c molecules. The European Physical Journal D-Atomic Molecular. Optical and Plasma Physics 12(1):147–151 Antoine R, Rayane D, Benichou E, Dugourd P h, Broyer M (2000) Electric dipole moment and charge transfer in alkali-c molecules. The European Physical Journal D-Atomic Molecular. Optical and Plasma Physics 12(1):147–151
Zurück zum Zitat Castellanos-Jaramillo A, Castellanos-Moreno A (2019) Bidimensional bound states for charged polar nanoparticles. J Nanoparticle Res 21(7):141CrossRef Castellanos-Jaramillo A, Castellanos-Moreno A (2019) Bidimensional bound states for charged polar nanoparticles. J Nanoparticle Res 21(7):141CrossRef
Zurück zum Zitat Connolly K, Griffiths DJ (2007) Critical dipoles in one, two, and three dimensions. Am J Phys 75(6):524–531CrossRef Connolly K, Griffiths DJ (2007) Critical dipoles in one, two, and three dimensions. Am J Phys 75(6):524–531CrossRef
Zurück zum Zitat Coon SA, Holstein BR (2002) Anomalies in quantum mechanics: the 1/r 2 potential. Am J Phys 70(5):513–519CrossRef Coon SA, Holstein BR (2002) Anomalies in quantum mechanics: the 1/r 2 potential. Am J Phys 70(5):513–519CrossRef
Zurück zum Zitat Crawford OH (1967) Bound states of a charged particle in a dipole field. Proc Phys Soc 91(2):279CrossRef Crawford OH (1967) Bound states of a charged particle in a dipole field. Proc Phys Soc 91(2):279CrossRef
Zurück zum Zitat Fernández FM (2014) Bound states of a charged particle in the field of an electric quadrupole in two dimensions. J Math Chem 52(6):1576–1580CrossRef Fernández FM (2014) Bound states of a charged particle in the field of an electric quadrupole in two dimensions. J Math Chem 52(6):1576–1580CrossRef
Zurück zum Zitat Fox K (1971) Simple approximate eigenfunctions for an electron in a finite dipole field. Phys Rev A 3(1):13CrossRef Fox K (1971) Simple approximate eigenfunctions for an electron in a finite dipole field. Phys Rev A 3(1):13CrossRef
Zurück zum Zitat Gutiérrez-López S, Castellanos-Moreno A, Rosas-Burgos RA (2008) A new constant of motion for an electric charge acted on by a point electric dipole. Am J Phys 76(12):1141–1145CrossRef Gutiérrez-López S, Castellanos-Moreno A, Rosas-Burgos RA (2008) A new constant of motion for an electric charge acted on by a point electric dipole. Am J Phys 76(12):1141–1145CrossRef
Zurück zum Zitat Herman R, Wallis RF (1981) Energy levels of an electron in the field of a finite electric dipole in a magnetic field. Phys Rev B 23(10):4902CrossRef Herman R, Wallis RF (1981) Energy levels of an electron in the field of a finite electric dipole in a magnetic field. Phys Rev B 23(10):4902CrossRef
Zurück zum Zitat Karamanis P, Pouchan C, Maroulis G (2008) Structure, stability, dipole polarizability and differential polarizability in small gallium arsenide clusters from all-electron ab initio and density-functional-theory calculations. Phys Rev A 77(1):013201CrossRef Karamanis P, Pouchan C, Maroulis G (2008) Structure, stability, dipole polarizability and differential polarizability in small gallium arsenide clusters from all-electron ab initio and density-functional-theory calculations. Phys Rev A 77(1):013201CrossRef
Zurück zum Zitat Kerimov GA, Ventura A (2010) Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem. Journal of Physics A: Mathematical and Theoretical 43(25):255304CrossRef Kerimov GA, Ventura A (2010) Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem. Journal of Physics A: Mathematical and Theoretical 43(25):255304CrossRef
Zurück zum Zitat Turner JE, Anderson VE, Fox K (1968) Ground-state energy eigenvalues and eigenfunctions for an electron in an electric-dipole field. Phys Rev 174(1):81CrossRef Turner JE, Anderson VE, Fox K (1968) Ground-state energy eigenvalues and eigenfunctions for an electron in an electric-dipole field. Phys Rev 174(1):81CrossRef
Zurück zum Zitat Van Zon R (2009) Effective pair potentials for spherical nanoparticles. Journal of Statistical Mechanics:, Theory and Experiment 2009(02):P02008 Van Zon R (2009) Effective pair potentials for spherical nanoparticles. Journal of Statistical Mechanics:, Theory and Experiment 2009(02):P02008
Zurück zum Zitat Wallis RF, Herman R, Milnes HW (1960) Energy levels of an electron in the field of a finite dipole. J Mol Spectrosc 4(1-6):51–74CrossRef Wallis RF, Herman R, Milnes HW (1960) Energy levels of an electron in the field of a finite dipole. J Mol Spectrosc 4(1-6):51–74CrossRef
Metadaten
Titel
Behavior of an electron in the vicinity of a tridimensional charged polar nanoparticle through a classical and quantum constant of motion
verfasst von
Alejandro Castellanos-Jaramillo
Sergio Gutiérrez-López
Arnulfo Castellanos-Moreno
Publikationsdatum
01.07.2020
Verlag
Springer Netherlands
Erschienen in
Journal of Nanoparticle Research / Ausgabe 7/2020
Print ISSN: 1388-0764
Elektronische ISSN: 1572-896X
DOI
https://doi.org/10.1007/s11051-020-04936-1

Weitere Artikel der Ausgabe 7/2020

Journal of Nanoparticle Research 7/2020 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.