In this M.Sc. Dissertation we have developed a formalism to obtain the solution of Schrödinger equation in a non-inertial frame. The frame is moving with an acceleration. The classical part of the formulation has been developed following Landau and Lifshitz [1] and obtained the single particle Hamiltonian. With the standard form of canonical quantization rule, we have setup the Schrödinger equation in non-inertial frame. See also the references [2–4] for some beautiful pedagogical discussion on non-inertial frame of reference. The physical situation of our study is basically the solution obtained by Fowler and Nordheim for the emission of electrons from cold metal surface under the action of strong electric field [7] known as cold field emission of electrons. However in the present formulation, it is the gravity, simulated by the acceleration acts on mass of the particle and causes emission. Hence we have got some flavor of Hawking radiation [8] and Unruh effect [9] within the limited scope of our non-relativistic approach.