Multichannel scattering problem with a nonseparable angular part as a boundary-value problem

Area of Science:

• Quantum mechanics
• Atomic physics
• Computational physics

Background:

• Solving quantum multichannel scattering problems with nonseparable angular parts is computationally challenging.
• Accurate approximations for wave functions and scattering parameters are crucial for understanding atomic collisions.

Purpose of the Study:

• To develop an efficient computational method for quantum multichannel scattering with nonseparable angular parts.
• To accurately approximate the angular part of the wave function and scattering parameters.
• To demonstrate the method's efficiency and applicability to specific physical phenomena.

Main Methods:

• Utilizing the nondirect product discrete-variable representation (DVR) for accurate angular approximation.
• Reducing the problem to a boundary-value problem solvable with efficient standard algorithms.
• Employing a block-band matrix for equation coefficients.

Main Results:

• The developed method provides an accurate approximation for the angular part of the wave function.
• The computational scheme demonstrates numerical efficiency, flexibility, and good convergence.
• Successfully applied to quantitatively describe Feshbach resonances in pair collisions in atomic traps and scattering in anisotropic traps.

Conclusions:

• The new computational method is efficient and accurate for solving complex quantum scattering problems.
• The approach is versatile and applicable to various phenomena, including Feshbach resonances and anisotropic scattering.
• The method lays groundwork for future investigations in quantum physics, such as spin-orbit coupling and dipolar confinement-induced resonances.