Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential

Under a perturbation by a decaying electric potential, the Landau Hamiltonian acquires some discrete eigenvalues between the Landau levels. We study the perturbation by an "expanding" electric potential \(V(t^{-1}x)\), \(t>0\), and derive a quasi-classical formula for the counting function of the discrete spectrum as \(t\to \infty\).