Quantum trajectories in complex space

Journal Article · Sun Jul 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.012115· OSTI ID:21011162

Chou, C -C; Wyatt, Robert E ^[1]

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1. Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712 (United States)

Quantum trajectories in complex space in the framework of the quantum Hamilton-Jacobi formalism are investigated. For time-dependent problems, the complex quantum trajectories determined from the exact analytical wave function for the free Gaussian wave packet and the coherent state in the harmonic potential are used to demonstrate that the information transported by the particles in the complex space can be used to synthesize the time-dependent wave function on the real axis. For time-independent problems, the exact complex quantum trajectories for the Eckart potential are obtained by numerically integrating the equations of motion. The unusual structure of the total potential (the sum of the classical and the quantum potentials) for the stationary states for the Eckart potential is pointed out. The variations of the complex-valued kinetic energy, classical potential, and quantum potential along the complex quantum trajectories are analyzed. This paper not only analyzes complex quantum trajectories for time-dependent and time-independent systems but also provides a unified description for complex quantum trajectories for one-dimensional problems in the quantum Hamilton-Jacobi formalism.

• OSTI ID: 21011162
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENSTATES
EQUATIONS OF MOTION
GAUSSIAN PROCESSES
HAMILTON-JACOBI EQUATIONS
HARMONIC POTENTIAL
KINETIC ENERGY
ONE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
TRAJECTORIES
WAVE FUNCTIONS
WAVE PACKETS