Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1611.03900

Wave functions for three electrons in a magnetic field

Héctor Mejía-Díaz, Daniel Julian Nader, Javier Alvarez‐Jimenez

Published Nov 11, 2016• 0 citations
arXivHTMLPDF

Abstract

This manuscript is in progress and the first version was removed by decision of the autors.
DOI
10.48550/arxiv.1611.03900

Related papers

Wave function of an electron in a magnetic field in the rotator approximation

B. V. Kholomai

Russian Physics Journal•Jan 1, 1977•0 citations

Instabilities of the Hubbard chain in a magnetic field

J. M. P. Carmelo, F. Guinea, Pedro D Sacramento

We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studying all response functions at low frequency \ensuremath{\omega} and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) \ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow} Fermi points, \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$. For finite values of the on-site repulsion U the instabilities occur for single \ensuremath{\sigma} electron added or removed at momenta \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$, for transverse spin-density wave (SDW) at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}}$ (where ${2\mathrm{k}}_{\mathrm{F}}$=${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$), and for a charge-density wave and SDW at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$ and \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}}$ SDW over all the remaining instabilities for a large domain of U and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transverse-spin response function in the fully polarized ferromagnetic phase.

arXiv:cond-mat/9701104•Physical review. B, Condensed matter•Mar 15, 1997•19 citations

Geometry of electron wave functions in the case of a zero magnetic quantum number

Yu. A. Aminov

Doklady Mathematics•Mar 1, 2014•0 citations

Proof of the Wave Function Identity, a New Symmetry Constraint for the Three-Electron Quantum Dot in a Magnetic Field and Ad Hoc Generalization to Bound Many-Electron Systems

Marlina Slamet, Viraht Sahni

We prove the Wave Function Identity (WFI), a new symmetry constraint on the solutions of the Schrödinger-Pauli equation for the Coulombically interacting N = 3 electron 2-dimensional harmonically bound ‘artificial atom’ or quantum dot in a uniform magnetic field. The symmetry is comprised of an interchange of the spatial coordinates of two electrons whilst keeping their spin moments unchanged, followed by an inversion of all three electron coordinates. The proof is achieved by first deriving the general form of the exact correlated wave function in the high-electron-correlation Wigner regime and then proving the WFI employing this form for a quartet state. The satisfaction of the Pauli principle (PP) and the odd parity of this state are also proved. An exact closed-form analytical expression for a quartet state in the Wigner regime is derived, and the properties of the PP, WFI, parity and other properties exhibited diagrammatically. Together with our prior proof of the WFI for the N = 2 electron case, we propose ad hoc the validity of the WFI for all bound-state N ≥ 2 electron systems for arbitrary symmetric binding potential, arbitrary electron-interaction of the form ω(|r – r’|) and arbitrary dimensionality.

Axioms•Oct 16, 2026•0 citations

On the Wave Functions of Many-Electron Systems

CRC Press eBooks•May 21, 2004•2 citations

Quantum mechanics in an axial magnetic field

J. Frenkel, John C. Taylor

We make three remarks about the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field (which we take to be parallel to the z-axis). First, when the field is uniform, we comment on the relation between the wave-function on the one hand if it is chosen to be an eigenstate of momentum (leaving aside the trivial z-dependence) and hence non-normalizable, and on the other hand if it is chosen to be an eigenstate of angular momentum. Second, we discuss the form of the wave-function when the magnetic field had a weak z-dependence. Finally, we make a short comment on the derivation of the diamagnetism of a free electron gas.

•Apr 30, 2004•0 citations
We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studying all response functions at low frequency \ensuremath{\omega} and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) \ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow} Fermi points, \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$. For finite values of the on-site repulsion U the instabilities occur for single \ensuremath{\sigma} electron added or removed at momenta \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$, for transverse spin-density wave (SDW) at momenta \ifmmode\pm\else\textpm\fi{}2kF{2\mathrm{k}}_{\mathrm{F}}2kF​ (where 2kF{2\mathrm{k}}_{\mathrm{F}}2kF​=${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$), and for a charge-density wave and SDW at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$ and \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse \ifmmode\pm\else\textpm\fi{}2kF{2\mathrm{k}}_{\mathrm{F}}2kF​ SDW over all the remaining instabilities for a large domain of U and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transverse-spin response function in the fully polarized ferromagnetic phase.
We prove the Wave Function Identity (WFI), a new symmetry constraint on the solutions of the Schrödinger-Pauli equation for the Coulombically interacting N = 3 electron 2-dimensional harmonically bound ‘artificial atom’ or quantum dot in a uniform magnetic field. The symmetry is comprised of an interchange of the spatial coordinates of two electrons whilst keeping their spin moments unchanged, followed by an inversion of all three electron coordinates. The proof is achieved by first deriving the general form of the exact correlated wave function in the high-electron-correlation Wigner regime and then proving the WFI employing this form for a quartet state. The satisfaction of the Pauli principle (PP) and the odd parity of this state are also proved. An exact closed-form analytical expression for a quartet state in the Wigner regime is derived, and the properties of the PP, WFI, parity and other properties exhibited diagrammatically. Together with our prior proof of the WFI for the N = 2 electron case, we propose ad hoc the validity of the WFI for all bound-state N ≥ 2 electron systems for arbitrary symmetric binding potential, arbitrary electron-interaction of the form ω(|r – r’|) and arbitrary dimensionality.
We make three remarks about the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field (which we take to be parallel to the z-axis). First, when the field is uniform, we comment on the relation between the wave-function on the one hand if it is chosen to be an eigenstate of momentum (leaving aside the trivial z-dependence) and hence non-normalizable, and on the other hand if it is chosen to be an eigenstate of angular momentum. Second, we discuss the form of the wave-function when the magnetic field had a weak z-dependence. Finally, we make a short comment on the derivation of the diamagnetism of a free electron gas.