Numerical construction of "optimal" nonoscillating amplitude and phase functions

Area of Science:

• Quantum mechanics
• Computational physics
• Scattering theory

Background:

• Constructing basis functions for quantum scattering processes can be challenging.
• Potentials with a single minimum require specialized numerical approaches.
• Existing methods may lead to oscillating amplitude and phase functions, complicating analysis.

Purpose of the Study:

• To develop a numerical recipe for generating non-oscillating amplitude and phase functions.
• To demonstrate the utility of these functions in bound-state scattering processes.
• To provide optimal functions analogous to classical action in semiclassical problems.

Main Methods:

• A numerical recipe is formulated for potentials exhibiting a single minimum.
• The method focuses on constructing non-oscillating amplitude and phase functions.
• Examples are provided to illustrate the recipe's application.

Main Results:

• A practical numerical recipe for constructing non-oscillating amplitude and phase functions is presented.
• The generated functions are shown to be useful for creating basis functions in scattering theory.
• The amplitude and phase functions are termed 'optimal' due to their non-oscillatory nature.

Conclusions:

• The proposed numerical recipe offers an effective way to obtain non-oscillating amplitude and phase functions.
• This method enhances the construction of basis functions for quantum defect theory and similar bound-state scattering problems.
• The 'optimal' functions provide a valuable tool for theoretical and computational physics research.