TITLE:
Wavelet Basis and Fourier Transform Approach to Path Integral Formulation of Electron Dynamics
AUTHORS:
Tommi Höynälänmaa
KEYWORDS:
Path Integral, Wavelet, Quantum Chemistry, Hydrogen Atom, Quantum Physics, Fourier Transform
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.10,
October
15,
2025
ABSTRACT: We present a method for the path integral formulation of electronic structure simulation. The time evolution operator is represented as matrix in a basis consisting of Deslauriers-Dubuc or Daubechies wavelets. We present an approximation of the path integral kernel and a method for calculating wavefunctions. The kernel is tested by finding wavefunctions and eigenenergies of one-dimensional and three-dimensional harmonic oscillators and hydrogen atom in one and three dimensions.