Quantum dynamics of wave packets in a Morse potential: A dynamical system approach

Area of Science:

• Quantum mechanics
• Dynamical systems theory
• Computational physics

Background:

• The Morse potential is a common model for molecular vibrations.
• Understanding quantum dynamics, including oscillations and escape, is crucial in molecular physics.
• Traditional methods may not fully capture complex quantum behaviors like tunneling.

Purpose of the Study:

• To investigate the applicability of a dynamical systems approach to quantum dynamics.
• To analyze quantum oscillations and escape phenomena in the Morse potential.
• To compare dynamical systems predictions with numerical solutions of the Schrödinger equation.

Main Methods:

• Applied a dynamical systems approach to model quantum dynamics.
• Performed direct numerical integration of the Schrödinger equation for comparison.
• Analyzed wave packet behavior, including mean position and variance, at various energies.

Main Results:

• The dynamical systems approach accurately reflects quantum dynamics in the Morse potential.
• A critical energy was identified, beyond which wave packet penetration into the classically forbidden region significantly increases.
• Instability in the dynamical system near the critical energy correlates with quantum escape phenomena.
• Quantum tunneling was clearly established at lower energies by comparing dynamical system outputs with classical bounds.

Conclusions:

• Dynamical systems theory provides valuable insights into quantum dynamics, particularly for the Morse potential.
• The approach successfully models wave packet escape and quantum tunneling.
• Unexpected relevance of dynamical systems highlights new avenues for studying quantum phenomena.