We develop a general formulation of quantum mechanics within the lowest Landau level in two dimensions. Making use of Bargmann’s Hilbert space of analytic functions we obtain a simple algorithm for the projection of any quantum operator onto the subspace of the lowest Landau level. With this scheme we obtain the Schrödinger equation in both real-space and coherent-state representations. A Gaussian interaction among the particles leads to a particularly simple form in which the eigenvalue condition reduces to a purely algebraic property of the polynomial wave function. Finally, we formulate path integration within the lowest Landau level using the coherent-state representation. The techniques developed here should prove to be convenient for the study of the anomalous quantum Hall effect and other phenomena involving electron-electron interactions.
Formalism for the quantum Hall effect: Hilbert space of analytic functions
Name of the Journal:
Phys. Rev. B
Proceedings, Conference, Subtitle or Series:
expanded and reprinted in: Physics in Noncommutative World I: Field Theories, edited by Miao Li and Yong-Shi Wu (Rinton Press, Princeton, NJ, 2002).
Date of Pub:
May 15, 1984
Year of Publication:
1984
Volume:
29
Issue:
10
Pages:
5617-5625
Abstract:
DOI Link: