• Corpus ID: 235727768

On the convergence of a novel family of time slicing approximation operators for Feynman path integrals

  title={On the convergence of a novel family of time slicing approximation operators for Feynman path integrals},
  author={S. Ivan Trapasso},
In this note we study the properties of a sequence of approximate propagators for the Schrödinger equation, in the spirit of Feynman’s path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a quadratic form in phase space, plus a bounded potential perturbation in the form of a pseudodifferential operator with a rough symbol. It is known that the corresponding Schrödinger propagator is a generalized metaplectic operator. This naturally motivates the… 



On the Pointwise Convergence of the Integral Kernels in the Feynman-Trotter Formula

We study path integrals in the Trotter-type form for the Schrödinger equation, where the Hamiltonian is the Weyl quantization of a real-valued quadratic form perturbed by a potential V in a class

Approximation of Feynman path integrals with non-smooth potentials

We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the

Schrodinger equations with rough Hamiltonians

We consider a class of linear Schrodinger equations in $\mathbb{R}^d$ with rough Hamiltonian, namely with certain derivatives in the Sjoostrand class $M^{\infty,1}$. We prove that the corresponding

On a (No Longer) New Segal Algebra: A Review of the Feichtinger Algebra

Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of functions with applications in time-frequency analysis, the theory of pseudo-differential operators and several

Mathematical theory of Feynman path integrals

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including

Semi-classical Time-frequency Analysis and Applications

This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in

Generalized metaplectic operators and the Schrödinger equation with a potential in the Sjöstrand class

It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by

Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics I

We give a theory of oscillatory integrals in infinitely many dimensions which extends, for a class of phase functions, the finite dimensional theory. In particular we extend the method of stationary