We present several new finite-difference schemes that can be used to numerically integrate the time-dependent Schrodinger equation. These schemes are explicit and use an Euler-type expression for the discrete time derivative. However, the second-order space derivative is modeled by a novel form not
Optimization of explicit symplectic schemes for time-dependent schrödinger equations
✍ Scribed by Xiaoyan Liu; Peizhu Ding; Jialin Hong; Lijin Wang
- Book ID
- 108076937
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 409 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0898-1221
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## Abstract The solution of the two‐dimensional time‐independent Schrödinger equation is considered by partial discretization. The discretized problem is treated as an ordinary differential equation problem and solved numerically by asymptotically symplectic methods. The problem is then transformed
Cheap and easy to implement fourth-order methods for the Schrodinger equation with time-dependent Hamiltonians are ïntroduced. The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative propert