High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schrödinger Equation
This work provides more accurate and robust numerical integration methods for solving the Schrödinger equation, which is important for quantum mechanics simulations.
The authors developed a new family of twelve-step linear multistep methods for integrating the Schrödinger equation, achieving improved phase-lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. Error analysis and numerical applications demonstrated the efficiency of the new methods.
In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schrödinger equation. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. This results in decreasing the sensitivity of the integration method on the estimated frequency of the problem. The efficiency of the new family of methods is proved via error analysis and numerical applications.