(2:45~3:15pm, Tea, Coffee, and Cookie)

Two seemingly distinct systems are analyzed and, somewhat unexpectedly, shown to be related.
System I - Electron in the field of a magnetic monopole: The problem is to find the states of a
(spinless) electron moving on a sphere and subject to a central magnetic field $B=g\frac{\hat r}{r^2}$.

As was shown by Dirac in 1931 [see also Wu and Yang, Phys. Rev. D 12, 3845 (1975)] the (so far elusive)
magnetic charge g and the electric charge e are related by the quantization condition 2eg = nħc (n = 1,2…is
the monopole number). In the continuum version, the problem was solved in 1931 by Igor Tamm.
I approach this problem from a "condensed matter point of view" using a tight binding model.
The energy spectrum is calculated analytically as function of n and displays a beautiful pattern,
which is entirely distinct from that of the Hofstadter buttery. The systematics of level degeneracy
is unusual and its analysis requires the construction of a theory of magnetic point symmetry groups.
The spectrum of an electron hopping on the sites of a Fullerene reveals a set of magic (monopole)
numbers ni.
System II - Electron in the field of a central charge: Spin-Orbit effects: The problem is to find the
states of a (spinfull) electron moving on a sphere subject to a central electric
field $E=q\frac{\hat r}{r^2}$.
In a continuum geometry, spin-orbit interaction results the familiar L.S coupling that affects atomic
spectra. In a tight binding formalism, on the other hand, it leads to peculiar Aharonov-Casher effect,
and the spectrum (calculated analytically) displays rich and beautiful pattern with some unexpected
symmetries in which physics and geometry interlace.
Connection between I and II: I expose a remarkable relation between the two seemingly distinct
physical problems: The energy spectrum in system II at a certain symmetry point is identical with the
energy spectrum in system I at n = 1. Thus, it is principally possible to test the physics of an
experimentally inaccessible system (magnetic monopole) in terms of an experimentally accessible
one (electron subject to spin-orbit force induced by central electric field).