Computation of multiple functional integrals in quantum physics

AbstractThe new method of computation of multiple functional integrals of quantum physics is elaborated. The method is based on the numerical integration over complete separable metric spaces via approximations exact on a class of polynomial functionals of given degree. New approximation formulas for the functional integrals with respect to Gaussian measure are constructed. The convergence of approximations to an exact value of integral is proved, the estimate of the remainder is obtained. In the particular case of conditional Wiener measure the approximation formulas with the weight are derived. The method is applied to the study of the multidimensional Calogero model and to computation of the binding of nucleons in the nucleus of tritium

Quantum Theory with Statistical Interpretation the Hydrogen-Like Atom Problem

In the paper the energy spectrum of the hydrogen like atom in the quantum mechanics with the non negative quantum distribution function (QDF) is studied. The essential spectrum of the Hamiltonian has been calculated. As for the eigenvalues situated beyond the essential spectrum, a method for numerical evaluation of their numbers and values is proposed. © 2001 IOS Press