EXPLICIT AND IMPLICIT NUMERICAL METHODS FOR TIME-DEPENDENT SCHR?DINGER EQUATION AND ERROR ANALYSIS
As one of the most significant equations in Quantum Mechanics,time-dependent Schrodinger equation can describe the evolution of wave function in different interaction poten-tial.The complicated forms of interaction potential make it generally impossible to find an an-alytical solution to the Schrödinger equation.Therefore,how to accurately numerically solve the time-dependent Schrödinger equation is of great significance for many physical problems.In this paper,emphasis is placed on how to solve Schrödinger equation with both explicit and implicit numerical methods,where the conclusion can be drawn that the wave function ob-tained by implicit method is more accurate than that of the explicit method based on the out-come of calculation.What's more,the deviation of implicit method can be proven to be con-vergent.In order to further explore the feasibility of the implicit scheme,this paper also a-dopts the screened potential at finite temperature and uses the implicit method to specifically solve the wave function evolution of charmonium.
time-dependent Schrödinger equationnumerical solution of partial differential e-quationstability analysis for explicit and implicit numerical methods
NETL
NSTL
万方数据
