Abstract:

The numerical solution for wave function evolution plays an important role in quantum mechanics research. Many numerical algorithms have been developed for time-independent potential fields. However, multiple physical problems exist with the time-dependent potential. In this case, previously developed algorithms cannot guarantee the unitary evolution of wave function. In this study, the Crank-Nicolson algorithm to maintain unitary evolution in time-dependent potential fields is developed with a fourth-order accurate Numerov algorithm used to achieve high-precision spatial discretization. A numerical test demonstrates that the new algorithm maintains the unitarity and stability of wavefunction evolution.

Key words: time-dependent potential energy, time-dependent Schr?dinger equation, Crank-Nicolson algorithm, Numerov algorithm