On size corrections to the diamagnetic susceptibility of a free electron gas

The magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/r _H, wherer _H is the radius of the classical electron orbit due to a constant magnetic fieldH. The magnetic moment is shown to be large and positive in the small size limitR/r _H?1 in agreement with recent experimental work, while in the usual large size limitR/r _H?1 the Landau susceptibility is obtained. The model is compared with a similar calculation in which a periodic boundary condition is applied in order to show explicitly how qualitative differences arise in the small size limit, and the relevance of the results to calculations for rectangular and spherical geometries with hard wall boundary conditions is examined.