The Path Integral Formulation: Bridging the Harmonic Oscillator and the Hydrogen Atom

Christopher C. Gerry, Akira Inomata

Nikom Choosiri, Virulh Sa-yakanit

Tommi Höynälänmaa

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.

Horacio Grinberg, Julio Marañón, H. Vucetich

The Kustaanheimo–Stiefel transformation together with the well-known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed.