Abstract
We review some applications of spectral methods based on Fourier expansions to computational problems in quantum mechanics and we discuss a single topic in some detail, namely the case of a quantum (charged) spinless particles on a Riemannian manifold interacting with a magnetic field (the problem of Landau levels in a curved configuration space). We study the asymptotic expansion of the ground state around the flat metric and we give an estimate of the first few coefficients.
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