Analytical Study of the Behavioral Trend of Klein-Gordon Equation in Different Potentials

In this work, we present the analysis of behavioral trend of Klein-Gordon Equation involving potential as regards when it comes to the study of particle, it has been observed that in every case of handling of KGE with potential of any type, it is made clear here that the equation has to first off all be transformed into a particular standard differential equation with a well-known solution which appears in form of implicitly defined transcendental equation. The equation on the other hand is to be solved analytically since the exact solution is not easily attainable without the use of mathematical tool especially when it comes to the consideration of the energy eigenvalue and the corresponding wave function because the solution is also always accompanied with a normalization constant often coupled with a condition that requires an arbitrarily chosen quantum number that come up when (l=0) and so on. In general, the analysis reveals the fact that the of trend of KGE involving potential gives a good understanding in the study of inter-molecular structure, diatomic crystals, and such case that involves inter-atomic interaction which is gives very nice idea in the study of bound state in atom.