A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated...

Area of Science:

• Computational physics and chemistry
• Quantum mechanics

Background:

• Solving the time-dependent Schrödinger equation is crucial for understanding quantum systems.
• Previous methods faced challenges with azimuthal asymmetries and computational efficiency.

Purpose of the Study:

• To present an efficient split-operator technique for solving the time-dependent Schrödinger equation.
• To address limitations of existing methods, particularly regarding azimuthal asymmetries and computational scaling.

Main Methods:

• Developed a split-operator technique in an angular coordinate system.
• Employed a fast spherical harmonics transform for efficient representation conversions.
• Incorporated adaptive time stepping and addressed the "m-mixing" problem.

Main Results:

• The method efficiently solves the time-dependent Schrödinger equation.
• Facile inclusion of azimuthal asymmetries (m-mixing) is achieved.
• The technique demonstrates favorable scaling and avoids explicit kinetic and potential energy matrix elements.

Conclusions:

• The presented technique offers an efficient and versatile approach for quantum dynamics simulations.
• This method advances the computational treatment of systems with azimuthal asymmetries.
• The technique's favorable scaling and reduced computational demands facilitate complex quantum mechanical problem-solving.