Communication: An exact short-time solver for the time-dependent Schrödinger equation

Area of Science:

• Quantum mechanics
• Computational chemistry
• Physical chemistry

Background:

• The time-dependent Schrödinger equation governs quantum system evolution.
• Accurate numerical methods are crucial for simulating quantum dynamics.
• Existing methods face challenges with precision and computational cost.

Purpose of the Study:

• To present an exact short-time integrator for the time-dependent Schrödinger equation.
• To apply this integrator to complex dynamics processes.
• To demonstrate its accuracy and efficiency for quantum simulations.

Main Methods:

• Utilizing an exact short-time integrator with Cayley's form (Padé (1,1) approximation).
• Implementing the integrator with a spectrally transformed Hamiltonian (Chen and Guo).
• Applying the method to calculate barrier penetration probability and laser-molecule interactions.

Main Results:

• The integrator achieves machine round-off accuracy for time-independent Hamiltonians.
• Accurate calculations of collision energy-dependent probability over a barrier were performed.
• The interaction between pulse laser and I(2) diatomic molecule was successfully simulated.

Conclusions:

• The developed short-time integrator offers a highly accurate and efficient tool for quantum dynamics.
• This method provides a reliable approach for simulating complex chemical and physical processes.
• The spectrally transformed Hamiltonian implementation enhances the integrator's applicability.