A STATISTICAL APPROACH TO QUANTUM MECHANICS

Aug, 1980
70 pages
Published in:
  • Annals Phys. 132 (1981) 427
Report number:
  • BNL-28588

Citations per year

1981199220032014202402468
Abstract: (Elsevier)
A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, | ψ 0 ( x )| 2 , the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.
  • QUANTUM MECHANICS: PATH INTEGRAL
  • APPROXIMATION: LATTICE
  • BOUNDARY CONDITION
  • MODEL: OSCILLATION
  • QUANTUM MECHANICS: ENERGY EIGENSTATE
  • PROPAGATOR
  • APPROXIMATION: EFFECTIVE POTENTIAL
  • FIELD EQUATIONS: INSTANTON
  • FIELD EQUATIONS: KINK
  • EFFECT: TUNNELING