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A numerical study of the effect of a perpendicular magnetic field on eigenstates is made for successive eigenmodes in devices with a symmetric crossbar geometry. The calculation was carried out by discretizing the Schr\"odinger equation with use of a symmetric gauge. Results show that the magnetic field splits the zero-field degenerate eigenvalues due to device symmetry and strongly mixes the corresponding eigenmodes.
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Weisz et al. (1990) studied this question.
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