Related papers: Path Integral Analysis of Arrival Times with a Com…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
The event reconstruction in high energy neutrino telescopes is based on the expression of the time delay distribution of the detected photons propagating to some distance from their emission point through a uniform and scattering medium.…
We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, simple moments of the distribution, such as the mean (MFPT)…
A time-dependent potential barrier has been used to probe the arrival-time distribution of the wave packet of a hot electron by raising the barrier to block the packet upon arrival of the packet at the barrier. To see whether the barrier…
String scattering amplitudes are typically expressed in formal integrals which diverge in physical kinematic regions. Recently the problem of divergence was cured by redefining integration contours. In this paper, we apply the new…
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model…
The general and explicit relation between the phase time and the dwell time for quantum tunneling or scattering is investigated. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, here we…
We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both…
The calculation of the decay rate of a metastable state in the path-integral formulation of stochastic processes is revisited. Previous derivations of this rate were achieved at the cost of a step that is difficult to justify…
Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
We present the very simple model of a particle detector and the proposal for the calculation of the average value of the time of arrival.
The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(\omega x)$ is obtained by solving path integrals. The method of delta functionals based on canonical and other transformations is used to reduce the path integral for…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
A novel integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys. Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential equation…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and…
We argue that under very general conditions, there is a significant complication in amplitudes for spacetimes regions constructed from path integrals. This is the fact that the concrete implementation of the restrictions on paths over an…
We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of…
Time of arrival refers to the time a particle takes after emission to impinge upon a suitably idealized detector surface. Within quantum theory, no generally accepted solution exists so far for the corresponding probability distribution of…