We consider the elastic scattering and bound states of charged quantum particles moving in the Aharonov-Bohm and an attractive ρ −2 potential in a partial wave approach. Radial solutions of the stationary Schrödinger equation are specified in such a way that the Hamiltonian of the problem is self-adjoint. It is shown that they are not uniquely fixed but depend on open parameters. The related physical consequences are discussed. The scattering cross section is calculated and the energy spectrum of bound states is obtained.
We consider the problem of self-adjoint extension of Hamilton operators for charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin solenoid). We present a pragmatic approach to the problem based on the orthogonalization of the radial solutions for different quantum numbers. Then we discuss a model of a scalar particle with a magnetic moment which allows to explain why the self-adjoint extension contains arbitrary parameters and give a physical interpretation.
We investigate the scattering of an electron by an infinitely thin and infinitely long straight magnetic flux tube in the framework of QED. We discuss the solutions of the Dirac and Maxwell fields in the related external pure AB potential and evaluate matrix elements and differential probabilities for the bremsstrahlung process. The dependence of the resulting cross section on the energy, direction and polarization of the involved particles is analyzed. In the low energy regime a surprising angular asymmetry is found which results from the interaction of the electron's magnetic moment with the magnetic field.
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