Berry phase, Group Structure of the Hydrogen Atom and the Coulombic Monopole in Non-commutative Quantum Mechanics

Rajhans, Juhi (2014) Berry phase, Group Structure of the Hydrogen Atom and the Coulombic Monopole in Non-commutative Quantum Mechanics. Masters thesis, Inidian Institute of Science Education and Research Kolkata.

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Abstract

This work introduces the reader to non-commutativity in quantum mechan- ics and explores the interaction picture of an electron and a monopole in the given scenario. It has been speculated that the unnatural vector po- tential in the case of a monopole magnetic �eld is due to the co-ordinate representation of the kinetic momentum operators. Thus if the co-ordinate representation is suitably constructed, one can generate a Hilbert space of self-adjoint operators which commute with the Hamiltonian. The �rst part of the work involves the study of the Berry phase and its manifestations in non-commutative quantum mechanics. The second part of the work involves the study of the group structure of the hydrogen atom and the preservation of the group structure in non-commutative quantum mechanics. The third part of the thesis deals with a charge-monopole interaction problem and the exact mapping of the group structure to the hydrogen atom problem. The concluding section gives a short description of the ongoing work of gener- alising the study of the group structure in the charge-monopole problem in non-commutative quantum mechanics.

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