β Scribed by Gary Scher; Malcolm Smith; Michel Baranger
No coin nor oath required. For personal study only.
We show that it is possible to do numerical calculations in elementary quantum mechanics using Feyrnnan path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical kesults for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient.
π SIMILAR VOLUMES
It is shown how matrix elements of the form \(\left\langle x\left|e^{-i f t}\right| y\right\rangle\), which arise in closed-form expressions for the generating functional, can be evaluated perturbatively using a path integral encountered in the quantum mechanics of a single particle. This allows one
The formation of on-site charge-density waves (CDWs) in the one-dimensional ( ID) Hubbard chain is studied by path-integral quantum Monte Carlo (QMC) simulations as a function of the band fdling, the ratio between on-site and nearest-neighbor intersite interaction as well as the net Coulomb interact