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Computation of the Eigenvalues of the Schr(?)dinger Equation by Symplectic Partitioned Runge-Kutta Methods

Author: ChenWenLi
Tutor: QiangWenChao
School: Xi'an University of Architecture and Technology
Course: Computational Mathematics
Keywords: Schr?dinger equation Triangle fitting Symplectic algorithm Sim block Runge-Kutta method Shooting method
CLC: O241.82
Type: Master's thesis
Year: 2009
Downloads: 232
Quote: 1
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Abstract


Schr?dinger equation is the fundamental equation of quantum mechanics , the different potential field radial Schrodinger equation is a second order differential equation , but only a few typical potential field Schr?dinger equation to get the analytical solution of the eigenvalue , so in solving other potential process of eigenvalues ??of Schr?dinger equation , numerical methods has caused a great deal of attention . approximate the effect of better methods in the process of research numerical solution for solving the Schr?dinger equation , many authors , for example , the progressive stack with the law , 1 / N expand other methods, it was also developed a mathematical software package applied to solve the numerical solution of the Schrodinger equation , these played a great role in promoting the continuous development of numerical solution of the Schr?dinger equation we know the Hamiltonian system can describe the nature of the physical process , suberic is one of the basic characteristics of the Hamilton system analog Hamiltonian system with conventional numerical methods , however , this feature is often destroyed due to the destruction of the important properties of , and often makes the numerical simulation fails , particularly in the long numerical simulation , the original problem beyond recognition. thus caused the attention of many scholars maintain symplectic structure of the Hamiltonian system algorithm , its application has important practical and theoretical significance in this article , we first review the basic theory of the symplectic algorithm as well as application of some the Xin block Runge-Kutta format in the calculation of the Schr?dinger equation eigenvalue , and then we construct two new triangular block fitting symplectic Runge-Kutta format we construct Singh respectively in the third part of the application calculate the numerical solution of the harmonic oscillator potential and Morse potential field next dimensional Schrodinger equation eigenvalue of in the fourth chapter , we summarize the results of the numerical solution of two potential field Schr?dinger equation , as well as some experience in the actual calculation for further outlook . Finally, the appendix gives this MATHEMATICA program .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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