In this paper, two second order half-linear difference equations are considered. By establishing their connections with a standard half-linear difference equation, we are able to obtain sufficient conditions for existence and nonexistence of eventually positive solutions.

In this paper, we primarily explore numerical solutions to the Quantum 1D Infinite Square Well problem, and the 1D Quantum Scattering problem. We use different finite difference schemes to approximate the second derivative in the 1D Schrodinger’s Equation and linearize the problem. By doing so, we convert the Infinite Well problem to a simple Eigenvalue problem and the Scattering problem to a s...