# An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

@article{Sakamoto2003AnEO, title={An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian}, author={Makoto Sakamoto and Shogo Tanimura}, journal={Journal of Mathematical Physics}, year={2003}, volume={44}, pages={5042-5069} }

We solved the Schrodinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus Tn=Rn/Λ is defined as a quotient of the Euclidean space Rn by an arbitrary n-dimensional lattice Λ. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schrodinger operator is assumed to be the Laplace…

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