Abstract
The exact eigenfunctions are found for an electron in a cylindrical container in the presence of a uniform axial magnetic field. The eigenvalue spectrum, while superficially similar to that in free space, is so essentially different that the statistical properties of an electron assembly in the cylinder are entirely different from those derived in previous work. It is therefore of interest to use an integration approximation in computing the energy of the assembly at 0\ifmmode^\circ\else\textdegree\fi{}K. It turns out to have a very strong size-dependent paramagnetic term, and the reasons for this are carefully explained. The work lends support to the view that the observed diamagnetism of electrons in the superconducting state cannot be understood in terms of any free-electron approximation, and that interactions with the lattice potential play an essential role.
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