Position scaling eigenfunctions are generated by transforming compactly supported orthonormal scaling functions and utilized for faster alternatives to maximally localized Wannier functions (MLWFs). The position scaling eigenfunctions are first applied to numerical procedures solving Schrödinger and Maxwell's equations, and the solutions well agree with the preceding results. Subsequently, by projecting the position scaling eigenfunctions onto the space spanned by the Bloch functions, approximated MLWFs are obtained. They show good agreement with the preceding results using MLWFs. In addition, analytical explanations of the agreements and an estimate of the error associated with the approximation are provided.

• Received 20 July 2023
• Revised 16 November 2023
• Accepted 20 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.245413