TITLE:
Angular Decomposition and Sign Solved Propagator of the 2D and 3D Helium Atom Path Integrals
AUTHORS:
Emmanouil George Thrapsaniotis
KEYWORDS:
Propagator, Angular Decomposition, Sign Problem, Central Limit Theorem, 3D Helium, 2D Helium
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.2,
February
25,
2022
ABSTRACT: In the present paper on the one hand we apply the central limit theorem to the solution of the sign problem of a path integral of two-interacting particles in potential and give an expression for the sign solved propagator (SSP) derived from that solution and on the other hand we perform the angular decomposition of the path integrals of the 2D and 3D Helium atoms. Finally, we combine those two results and derive the SSPs of the 2D and 3D Helium atoms.