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Colloquim
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Eigenvalue problem for the Aharonov-Bohm Hamiltonian on a 2-torus YABU Yoshiro 22nd Oct (Fri) 13:30-
The eigenvalue problem is considered for the Aharonov-Bohm Hamiltonian that is defined on a two-torus with a singular vector potential for the magnetic field describing $N$ solenoids. The eigenvalue and associated eigenfunctions are given in explicit forms if each flux of solenoids is quantized. It is also shown that the deficiency indices of the Hamiltonian are twice the number of solenoids with non-quantized fluxes. This implies that the Hamiltonian is not essentially self-adjoint if there is a solenoid with non-quantized flux. |
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