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

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Theoretical Physics

Background:

• The semiclassical coherent state propagator is crucial for approximating quantum dynamics.
• Existing methods for calculating the propagator can be computationally intensive and suffer from issues like caustics.

Purpose of the Study:

• To present a new derivation and analytic expression for the semiclassical coherent state propagator.
• To develop a final value representation that overcomes limitations of current approaches.
• To demonstrate the method's efficacy using the 1D Morse oscillator.

Main Methods:

• A novel derivation of Huber and Heller's method for complex root trajectories, starting from the time-dependent Schrödinger equation.
• Derivation of an analytic expression for the semiclassical coherent state propagator with a simplified prefactor.
• Formulation of a final value representation for the time-dependent wavefunction.

Main Results:

• The new derivation allows for broader generalizations of the semiclassical formalism.
• The analytic expression requires solving fewer equations of motion compared to alternatives.
• The final value representation successfully avoids root searches, eliminates caustics, and includes interference automatically.

Conclusions:

• The presented developments offer significant improvements in calculating the semiclassical coherent state propagator.
• The new method shows potential as an attractive alternative to existing semiclassical techniques for quantum dynamics.
• Numerical results for the 1D Morse oscillator validate the effectiveness of the proposed approach.