For a densely defined self-adjoint operator H in Hilbert space F the operator exp⁡(− it H) is
the evolution operator for the Schrödinger equation i ψ t′= H ψ, ie if ψ (0, x)= ψ 0 (x) then ψ …

This survey describes the method of approximation of operator semigroups, based on the
Chernoff theorem. We outline recent results in this domain as well as clarify relations …

A Feynman formula is a representation of a solution of an initial (or initial-boundary) value
problem for an evolution equation (or, equivalently, a representation of the semigroup …

Evolution semigroups generated by pseudo-differential operators are considered. These
operators are obtained by different (parameterized by a number τ) procedures of …

This note is devoted to the approximation of evolution semigroups generated by some
Markov processes and hence to the approximation of transition probabilities of these …

We consider operator semigroups generated by Feller processes killed upon leaving a
given domain. These semigroups correspond to Cauchy–Dirichlet type initial-exterior value …

In the paper we derive two formulas representing solutions of Cauchy problem for two
Schrödinger equations: one-dimensional momentum space equation with polynomial …

We present a definition for tomographic Feynman path integral as representation for
quantum tomograms via Feynman path integral in the phase space. The proposed …

This note is devoted to quantum tomograms application in quantum information science.
Representation for quantum tomograms of continuous variables via Feynman path integrals …

A method to describe classical and quantum evolution systems is presented. The method is
based on the so-called Feynman formulae, ie on representations of solutions of evolution …