Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
J Chem Phys. 2010 Jan 7;132(1):014112. doi: 10.1063/1.3289728.
The quantum trajectory dynamics is extended to the wave function evolution in imaginary time. For a nodeless wave function a simple exponential form leads to the classical-like equations of motion of trajectories, representing the wave function, in the presence of the momentum-dependent quantum potential in addition to the external potential. For a Gaussian wave function this quantum potential is a time-dependent constant, generating zero quantum force yet contributing to the total energy. For anharmonic potentials the momentum-dependent quantum potential is cheaply estimated from the global Least-squares Fit to the trajectory momenta in the Taylor basis. Wave functions with nodes are described in the mixed coordinate space/trajectory representation at little additional computational cost. The nodeless wave function, represented by the trajectory ensemble, decays to the ground state. The mixed representation wave functions, with lower energy contributions projected out at each time step, decay to the excited energy states. The approach, illustrated by computing energy levels for anharmonic oscillators and energy level splitting for the double-well potential, can be used for the Boltzmann operator evolution.
量子轨迹动力学扩展到虚时的波函数演化。对于无节点波函数，一个简单的指数形式导致了轨迹的类经典运动方程，除了外势外，还代表了波函数中的动量相关量子势。对于高斯波函数，这种量子势是一个时变常数，产生零量子力，但对总能量有贡献。对于非谐势，从泰勒基的轨迹动量的全局最小二乘拟合中可以廉价地估计动量相关量子势。在几乎不增加计算成本的情况下，在混合坐标空间/轨迹表示中描述有节点的波函数。由轨迹集合表示的无节点波函数衰减到基态。混合表示的波函数，在每个时间步将较低的能量贡献投影出来，衰减到激发的能量状态。该方法通过计算非谐振荡器的能级和双势阱的能级分裂来说明，可以用于玻尔兹曼算子演化。
