Browsing by Author "Groenewald, Hendrikus Wilhelm"
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- ItemNon-commutative quantum mechanics in 3-dimensional fuzzy space and its applications(Stellenbosch : Stellenbosch University, 2018-03) Groenewald, Hendrikus Wilhelm; Scholtz, Frederik G.; Kriel, Johannes N.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH SUMMARY: As the structure of space-time at very short length scales comparable to the Planck length remains a contentious issue, this study aims to determine whether non-commutative space-time would prove to be an appropriate candidate for space-time at short length scales. Also, it aims to test whether it would be possible to observe non-commutative e ects on macroscopic scales. By providing a formulation for quantum mechanics where fuzzy commutation relations for spatial coordinates are assumed, this study was able to make notable progress toward this goal. Exact solutions to the non-commutative free particle and spherical well problems were achieved and e ects exclusive to non-commutative systems were observed, in particular an upper bound on the kinetic energy of a particle and a nite number of bound states in the spherical well problem. Signi cant deviations from the normal behaviour of commutative systems were also observed in the study of scattering states of the fuzzy well where states with high incident energies experience the spherical well as a repulsive potential. Finally, thermodynamic studies of non-interacting fermions con ned in fuzzy space provided drastically di erent results for high energy, high particle density and low temperature systems in comparison to standard results. These results include an incompressibility limit for the fermion gas, as well as an apparent duality between high density and low density systems.