Numerical investigation of multidimensional quantum systems by approximate functional integration

The method of computation of characteristics of quantum systems with many degrees of freedom by numerical integration in functional spaces is elaborated. For the multiple functional integrals with Gaussian measures in the full separable metric spaces the approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. Under determined conditions the convergence of approximations to exact value of integral is proved, the speed of convergence is estimated. The efficiency of method is studied on example of multidimensional quantum oscillator. The binding energy of particles in the nucleus of tritium is computed. The comparison of the numerical results with the data obtained by the other authors in the framework of different approaches (variational, Monte Carlo) demonstrates the advantages of our method.