Non-Commutative Quantum Mechanics

In this thesis we have summarized the background of non-commutative quantum mechanics. We have also loosely touched the related topics. Non-commutativity in quantum mechanics completely changes our understanding of the phase space and has the potential to explain multiple problems in different branches of physics. This makes it a very significant topic to research. As an example we have calculated the Landau Problem well-known commutative setting, and the non-commutative setting. From these results we can see that in the presence of sufficiently strong magnetic fields it is possible to measure q and h may be experimentally accessible. Due to the symmetry of the problem, we show that the addition of an electric field perpendicular to the magnetic field has no effect on the Landau levels for commutative and non-commutative settings.