Communication: Overcoming the root search problem in complex quantum trajectory calculations

Journal Article · Tue Jan 28 04:00:00 EST 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4862898· OSTI ID:22255222

Zamstein, Noa; Tannor, David J. ^[1]

---

1. Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)

Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987)]. Our method proceeds directly from the time-dependent Schrödinger equation and therefore allows various generalizations of the formalism. Second, we obtain an analytic expression for the semiclassical coherent state propagator. We show that the prefactor can be expressed in a form that requires solving significantly fewer equations of motion than in alternative expressions. Third, the semiclassical coherent state propagator is used to formulate a final value representation of the time-dependent wavefunction that avoids the root search, eliminates problems with caustics and automatically includes interference. We present numerical results for the 1D Morse oscillator showing that the method may become an attractive alternative to existing semiclassical approaches.

• OSTI ID: 22255222
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 140; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
EIGENSTATES
EQUATIONS OF MOTION
INTERFERENCE
OSCILLATORS
PROPAGATOR
SEMICLASSICAL APPROXIMATION
TIME DEPENDENCE
WAVE FUNCTIONS