相关论文: Feynman integrals for a class of exponentially gro…
We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F} = \frac{1}{4} F_{\mu\nu}F^{\mu\nu} (x)$,…
We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
We present the quantum mechanics problem of the one-dimensional Schroedinger equation with the trigonometric Rosen-Morse potential. This potential is of possible interest to quark physics in so far as it captures the essentials of the QCD…
The Schr\"odinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order…
In this paper, the Feynman path integral formulation of the continuous-continuous filtering problem, a fundamental problem of applied science, is investigated for the case when the noise in the signal and measurement model is additive. It…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified…
we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the $L^2$ transition probability amplitude via…
This work is devoted to non-linear stochastic Schr\"odinger equations with multiplicative fractional noise, where the stochastic integral is defined following the Riemann-Stieljes approach of Z\"ahle. Under the assumptions that the initial…
We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a…
We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…
We prove the existence of weak solutions in the space of energy for a class of non-linear Schroedinger equations in the presence of a external rough magnetic potential. Under our assumptions it is not possible to study the problem by means…
Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave…
We prove the existence and uniqueness of invariant measures for the fractional stochastic Burgers equation (FSBE) driven by fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the…
We construct global-in-time singular dynamics for the (renormalized) cubic fourth order nonlinear Schr\"odinger equation on the circle, having the white noise measure as an invariant measure. For this purpose, we introduce the…
We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their…