期刊
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷 -, 期 -, 页码 -出版社
WILEY
DOI: 10.1002/num.23006
关键词
asymptotic Green's function; effective mass; exponential integration; fast Fourier transform; Krylov subspace; Schrodinger equation; WKBJ
In this study, operator splitting-based numerical methods are introduced to solve the time-dependent Schrodinger equation with a position-dependent effective mass. The wavefunction is propagated either by the Krylov subspace method-based exponential integration or by an asymptotic Green's function-based time propagator. These methods have complexity O(NlogN) per step with appropriate algebraic manipulations and fast Fourier transform, where N is the number of spatial points.
Numerical solution of the time-dependent Schrodinger equation with a position-dependent effective mass is challenging to compute due to the presence of the non-constant effective mass. To tackle the problem we present operator splitting-based numerical methods. The wavefunction will be propagated either by the Krylov subspace method-based exponential integration or by an asymptotic Green's function-based time propagator. For the former, the wavefunction is given by a matrix exponential whose associated matrix-vector product can be approximated by the Krylov subspace method; and for the latter, the wavefunction is propagated by an integral with retarded Green's function that is approximated asymptotically. The methods have complexity O(NlogN)$$ O\left(N\log N\right) $$ per step with appropriate algebraic manipulations and fast Fourier transform, where N$$ N $$ is the number of spatial points. Numerical experiments are presented to demonstrate the accuracy, efficiency, and stability of the methods.
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