The Passage of Bound state and Resonance across a Barrier

The passage of a composite object across a barrier is very important for reaction physics in areas such as nuclear physics, condensed matter physics and other fields. In this report, we approach the problem of the passage a composite object across a barrier by addressing the state of a particle and its dynamics in a potential well or hitting a barrier. We provide a numerical solution to the one dimensional time-dependent Schrödinger equation using the Crank-Nicolson method. The Bound state of a proton is demonstrated. We also demonstrate a proton hitting a rectangular potential barrier. The tunneling phenomenon is observed. Transmission and Reflection probabilities were determined. Finally, the model for a composite object across a barrier is formulated.