Study Of Wave Packet Dynamics Based On Bohmian Mechanics

Since de Broglie proposed the wave-particle duality,research on the theory and application of wave packet dynamics has always been a hot spot.The development of femto-second laser technology,enables the lab to the preparation of femto-second laser pulses,and the chemical bond rupture and forming process can be observed through the pump-probe technique,which have uncovered the veil of the super fast reaction dynamics and also made the research of wave packet dynamics to become a hot spot.Wave packet dynamics study can not only help us know about the characteristics of particle movement,and also enable us to control some of atom-molecular reaction process by controlling the impact of various external conditions on the movement of the wave packet.Our research based on bohmian mechanics study the dynamics of wave packet in various external field and obtain the bohmian particle trajectory.David Bohm proposed bohmian mechanics in 1953 as a different interpretation of quantum mechanics.Assuming the existence of quantum potential,This method realized the transition from classical Hamilton-Jacobi theory to quantum theory,which made it more simple and concise;Traditional quantum theory solve the wave function in configuration space which made it very abstract and not physically apparent.In contrast,bohmian mechanics obtain the particle trajectory in real space,which illustrate the evolution of spatial probability distribution in a more direct way.In this paper,we collect the numerical method of bohmian mechanics,and compared bohmian mechanics with quantum mechanics in the interpretations of particle motion.We computed the quantum trajectory by solving the propagation of quantum trajectory method algorithm(QTM).As to the free evolution of wave packet,we analyzed wave packet dispersion in bohmian picture.We found the harmonic vibration of wave packet under harmonic oscillator potential in a particular way.We proposed a new method to calculate derivatives on un-structured mesh.We numerically simulated electronic wave packet movement in laser-incident one-dimensional hydrogen atom,which can prove semi-classical three-step model strong field physics research and also prove that the method can be generalized.