## SPEEDUP codes for Phys. Rev. E 79 (2009) 036701

Codes used in:

A. Balaz, A. Bogojevic, I. Vidanovic, and A. Pelster

"Recursive Schrödinger Equation Approach to Faster Converging Path Integrals"

arXiv e-print: 0806.4774

The following Mathematica codes were written for this paper:Calculation of many-body effective action for a general potential:

Mathematica notebook and p=10 result

Calculation of a single-particle one-dimensional effective action for a general potential:

Mathematica notebook and p=35 result

Calculation of the velocity independent part of a single-particle one-dimensional effective action for a general potential:

Mathematica notebook and p=37 result

Calculation of a single-particle one-dimensional effective action for an anharmonic oscillator with the quartic coupling:

Mathematica notebook and p=144 result

Calculation of a single-particle one-dimensional effective action for the modified Pöschl-Teller potential:

Mathematica notebook and p=41 result

A. Balaz, A. Bogojevic, I. Vidanovic, and A. Pelster

"Recursive Schrödinger Equation Approach to Faster Converging Path Integrals"

*Phys. Rev. E***79**(2009) 036701arXiv e-print: 0806.4774

By recursively solving the underlying Schrödinger equation, we set up an efficient systematic approach for fast converging Monte Carlo calculations of path integrals. With this we obtain discrete-time effective actions for both one and many particles in arbitrary dimension to orders which have not been accessible before. The derived effective actions are given as series in the time of propagation ε, and ensure the convergence to the continuum as fast as ε

^{p}. Currently available results are*p*=10 level effective action for a general many-body theory, and*p*=35 for a single particle moving in one dimension. For several specific classes of potentials one can calculate even higher order effective potentials, as can be seen below.The following Mathematica codes were written for this paper:

Mathematica notebook and p=10 result

Mathematica notebook and p=35 result

Mathematica notebook and p=37 result

Mathematica notebook and p=144 result

Mathematica notebook and p=41 result