Trajectory approach to the Schrodinger-Langevin equation with linear dissipation for ground states

作者：Chou Chia Chun^*

来源：Annals of Physics, 2015, 362: 57-73.

DOI：10.1016/j.aop.2015.07.027

• Schrodinger-Langevin equation
• Bohmian trajectory
• Complex quantum Hamilton-Jacobi equation
• Linear dissipation
• Ground state

The Schrodinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrodinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.

• 出版日期2015-11
• 单位清华大学