Feynman-Kac path integral calculation of the ground state energy of atoms

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:6923607

Orr, D E

In a paper written in 1950, the mathematician, Marc Kac, established a rigorous basis for the Feynman path-integral formulation of quantum mechanics. The original Feynman path integral lacks mathematical rigor in the definition of [open quotes]summing over all paths[close quotes], which are infinite in number (a theorem by Cameron states that a finite, real or complex, Lebesgue measure of the path defined by Feynman does not exist). The difficulty of using Feynman's method in a computation is supported by the observation that an accurate path integral solution of the hydrogen groundstate was only recently computed (in 1984). Since its introduction in 1950, the Feynman-Kac path integral (FKPI) has received limited attention despite its simplicity and power in solving quantum many-body problems. This work demonstrates that the FKPI method can be used to find the ground state and excited states of small atomic systems to within experimental accuracy, and is ideally suited for the new massively parallel computer architectures, such as Thinking Machines CM-5, the INTEL Paragon, et al., or can be effectively used in a cluster of loosely-coupled workstations. It also demonstrates a simple procedure for incorporating into the FKPI computational method restrictions on the many-body wavefunction imposed by permutation symmetries of identical particles.

• Research Organization: Texas Univ., Arlington, TX (United States)
• OSTI ID: 6923607
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
664000* -- Atomic & Molecular Physics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
COMPUTER CALCULATIONS
ENERGY LEVELS
FEYNMAN PATH INTEGRAL
GROUND STATES
INTEGRALS
MANY-BODY PROBLEM
PARALLEL PROCESSING
PROGRAMMING