Solution of atomic orbitals in an interpolating wavelet basis.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Atomic Physics

Background:

• Solving the Schrödinger and Hartree-Fock equations is crucial for understanding atomic structure.
• Traditional methods can be computationally intensive, especially for many-electron systems.
• Wavelet-based approaches offer potential for improved efficiency and accuracy.

Purpose of the Study:

• To apply interpolating wavelets as basis functions for solving atomic structure equations.
• To develop and implement methods for handling operators in wavelet basis sets.
• To investigate the convergence properties of atomic parameters using this novel approach.

Main Methods:

• Utilized interpolating wavelets as basis functions for the Schrödinger and Hartree-Fock equations.
• Employed a nonstandard operator form for computations across multiple resolution levels.
• Developed an algorithm for converting matrices between nonstandard and standard operator forms.
• Derived analytic formulas for evaluating Hamiltonian and Fock operator components.

Main Results:

• Successfully solved equations for hydrogenic and several many-electron atoms (He, Li, Be, Ne, Na, Mg, Ar).
• Demonstrated the convergence of atomic parameters, such as orbital eigenvalues, with increasing resolution levels.
• Validated the efficiency and accuracy of the wavelet-based approach.

Conclusions:

• Interpolating wavelets provide an effective basis set for atomic structure calculations.
• The developed methods and algorithms facilitate accurate and efficient computations.
• This approach shows promise for advancing quantum chemistry and atomic physics simulations.