Bohm's formulation in imaginary time: estimation of energy eigenvalues

Abstract

Bohm's hydrodynamic formulation of quantum mechanics is employed to solve the diffusion equation. Quantum trajectories are found to behave differently in imaginary time, exhibiting caustic singularities. A wavefunction repartitioning methodology is introduced to prevent the imaginary-time crossing events, leading to stable evolution that does not suffer from the numerical obstacles that characterize Bohmian dynamics in real time. Use of an approximate technique based on trajectory stability properties to solve Bohm's equations in imaginary time leads to an accurate prediction of the energy of a low-lying eigenstate from a single quantum trajectory.

Acknowledgement

This work was supported by the National Science Foundation under award no. CHE-0212640.