High Accuracy Numerical Calculation Of Some Problems In Quantum Mechanics

Molecular reaction dynamics can be used to study the nature of chemical reactions at the atomic and molecular levels.Theoretically,the time-dependent wave packet method has become a very important research method.In this paper,the numerical solution method of quantum dynamics in the field of non-relativity and the lattice distribution method are introduced.Spectral difference and sin-DVR and FE-DVR methods play an important role in the development of theoretical calculation methods.Secondly,the nuclear motion of the general molecule often occurs on the adiabatic potential energy surface.When there is a conical intersection,the Hamilton quantity needs to introduce diagonal Born-Oppenheimer correction(DBOC)and geometric phase(GP)addition terms.It is verified for the first time that the sinc-DVR method can obtain reliable results when the conical intersection energy is not dealt with when the energy of the conical intersection is high under the adiabatic representation,and there is no comparison between the two methods.The effect is poor when any vector potential of geometric phase is entered.Finally,there are few numerical methods in the field of relativity,and the Klein-Gordon equation and the Dirac equation are mainly used to deal with the particle motion with the relativistic effect,here a sparse band matrix is introduced,and the combination of the spectral difference and the OFE-DVR and the real-space split operator method is used in the numerical calculation of the Klein-Gordon equation.The lattice efficiency and the computational efficiency are improved,and the motion of the Gaussian wave packet in the vibration potential of the laser field and the harmonic oscillator is simulated,andthe sine-DVR method is developed for the numerical calculation of the Dirac equation,and the Klein paradox phenomenon is used to verify.The correctness of the Dirac equation is obtained,and the scattering of electrons and neutrinos in the step potential is calculated effectively,and their wave packet states in the laser field are simulated accordingly.