### Abstract

The Schrödinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential. For tracking realizations in a two-dimensional electron gas, the degeneracy of the lowest Landau level persists and the "tracking" solutions span the ground state subspace. In the context of the fractional quantum Hall problem, the Laughlin wave function is shown to be a tracking solution. Tracking solutions for screened Coulomb interactions are also constructed. The resulting wave functions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

Original language | English |
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Pages (from-to) | 1405-1413 |

Number of pages | 9 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 58 |

Issue number | 3 |

Publication status | Published - Jul 15 1998 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*58*(3), 1405-1413.

**Interacting electrons in magnetic fields : Tracking potentials and Jastrow-product wave functions.** / Fáth, G.; Haley, Stephen B.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 58, no. 3, pp. 1405-1413.

}

TY - JOUR

T1 - Interacting electrons in magnetic fields

T2 - Tracking potentials and Jastrow-product wave functions

AU - Fáth, G.

AU - Haley, Stephen B.

PY - 1998/7/15

Y1 - 1998/7/15

N2 - The Schrödinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential. For tracking realizations in a two-dimensional electron gas, the degeneracy of the lowest Landau level persists and the "tracking" solutions span the ground state subspace. In the context of the fractional quantum Hall problem, the Laughlin wave function is shown to be a tracking solution. Tracking solutions for screened Coulomb interactions are also constructed. The resulting wave functions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

AB - The Schrödinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential. For tracking realizations in a two-dimensional electron gas, the degeneracy of the lowest Landau level persists and the "tracking" solutions span the ground state subspace. In the context of the fractional quantum Hall problem, the Laughlin wave function is shown to be a tracking solution. Tracking solutions for screened Coulomb interactions are also constructed. The resulting wave functions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.

UR - http://www.scopus.com/inward/record.url?scp=0038704307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038704307&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 1405

EP - 1413

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 3

ER -