Koroto, Tesfaye2018-07-052023-11-092018-07-052023-11-091992-06http://10.90.10.223:4000/handle/123456789/6642This study is broadly divided into two parts. The first deals with a set of useful results in non-relativistic quantum mechanics that prove to be useful in a variety of contexts. Although elementary, they have remained obscure for a long time. The advent of quarkonium spectroscopy has basically revealed their importance. The second part considers the quantum discontinuity phenomenon. Its origin is carefully traced. Two original partially exactly solvable models are proposed that exhibit such a phenomenonenQuantum Discontinuity PhenomenonThesis