Solving the schrodinger equation for different potential barriers.

Abstract

Schrodinger equation is a linear partial differential equatiion that governs the wave function of quantum mechanical system. It is a key result in quantum mechanics and its discovery was a significant landmark in the development of the subject, schrodinger equation is named after Erain Schrodinger who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel prize in physics in 1933. Conceptually, the schrodinger equation is the quantum counter part of Newton’s second law in classical mechanics. Given a set of known initial conditions, Newton’s second law makes a mathematical predication as to what path a given the evolution over time of a wave function, the quantum mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time - evolution operator must be unitary and must therefore be generated by the exponential of a self-adjoint operator which is the quantum Hamiltonian. The schrodinger equation is sometimes called wave mechanics