Understanding the temporal evolution of the wave function in the proton tunneling reactions allows us to make theoretical predictions on the possible femtosecond spectroscopy patterns. However, the analytical solution of the time-dependent Schrödinger equation of complex molecules is challenging and requires a high computational cost. In this study, we solve the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method, highlighting its simplicity of calculation, even for multidimensional tunneling reactions. The obtained model is applied to studying malonaldehyde's two-dimensional intramolecular proton tunneling, comparing the results with those obtained using other computational methods.

中文翻译：

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研究瞬态薛定谔方程中的质子隧道动力学

了解质子隧道反应中波函数的时间演化使我们能够对可能的飞秒光谱模式进行理论预测。然而，复杂分子的瞬态薛定谔方程的解析解具有挑战性，并且需要很高的计算成本。在本研究中，我们使用傅里叶网格哈密顿方法求解瞬态薛定谔方程，突出了其计算的简单性，即使对于多维隧道反应也是如此。所获得的模型应用于研究丙二醛的二维分子内质子隧道效应，并将结果与​​使用其他计算方法获得的结果进行比较。