Method for evaluating one-dimensional path integrals

A practical method is developed for calculating numerically one-dimensional path integrals for an arbitrary potential $V\left(x\right)\mathrm{}$. For the oscillator potential $V\left(x\right)=\frac{k{x}^2}{2}$ the well-known analytic solution is obtained. To illustrate the numerical convergence of this method the path integral for the Ginzburg-Landau potential, $V\left(x\right)=-\frac{A{x}^2}{2}+\frac{B{x}^4}{4}$, is calculated over a range of the positive constants $A$ and $B$ and compared with numerical solutions of the Schrödinger equation.