The implementation of an improved differential transform scheme on the Schrodinger equation governing wave-particle duality in quantum physics and optics
Kingsley Timilehin Akinfe, Adedapo Chris Loyinmi
Abstract
Seeking solutions to nonlinear differential equations cannot be overemphasized as this illuminates clarity in the dynamical behavior of the described model, and thus, enables precise forecasting of the processes with respect to time. In this study, Elzaki integral transform as a means to complement domain decomposition for a more convergent result has been coupled with the projected differential transform viz: an improved differential transform scheme, to solve the renowned Schrodinger equation derived from the quantum physics, waves, and field theory; describing the mechanics of wave-particle duality, quantum entanglement, energy quantization, motions of optical waves; consequently applicable in quantum mechanics, fluid dynamics, quantum field theory, solid-state physics, plasma physics, Optics, reaction-diffusion theory, interest rate dynamics, shock-wave formation, quantum computing, financial modeling, quantum finance, and so on. Achieved results from the implementation of this method through tables, convergence plots, and other graphical illustrations when the mass of the particle and constant of proportionality in the system is varied arbitrarily revealed quite an excellent convergence to the exact solution, rich in reliability than existing works of literature while an increase in the mass of the particle induces a contraction of the surface area of the complex system whilst decreasing the radical axis of concentric circles, and notably, an increase in proportionality constant decreases the spiral effect of the system and all plots tend to converge as this increases.