Wilkinson, Michael An exact effective Hamiltonian for a perturbed Landau level. (English) Zbl 0639.47010 J. Phys. A 20, 1761-1771 (1987). The two-dimensional problem of the influence of a scalar potential V(x,y) on a Landau level is represented by an exact one-dimensional effective Hamiltonian, valid provided the gaps between the n th Landau levels remain open and the matrix of the projection operator for the n th perturbed level is nonsingular. The effective Hamiltonian can be expressed as a power series in \(V/E_ c\), where \(E_ c\) is the cyclotron energy. The phase space function \(H^{(x)}_{eff}(x,p)\) resembles the potential V(x,y) and when the area of a flux quantum is much smaller than the characteristic length scale of V, then \(H\to V\). The effective Hamiltonian preserves the translational and rotational symmetries of V exactly, but reflection symmetries are retained only in the lowest order of the perturbative expansion. Reviewer: O.Gherman Cited in 8 Documents MSC: 47A55 Perturbation theory of linear operators 46N99 Miscellaneous applications of functional analysis 81Q15 Perturbation theories for operators and differential equations in quantum theory Keywords:symmetries of the Hamiltonian; influence of a scalar potential; Landau level; cyclotron energy; area of a flux quantum; translational and rotational symmetries; perturbative expansion × Cite Format Result Cite Review PDF Full Text: DOI Link