Related papers: Scattering by a reflectionless modified P\"oschl-T…
Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically…
The conditions for optimal reflection-free complex-absorbing potentials (CAPs) are discussed. It is shown that the CAPs as derived from the smooth-exterior-scaling transformation of the Hamiltonian,[J. Phys. B. 31, 1431 (1998)], serve as…
We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions…
We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a…
Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive…
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…
The phenomenon of wavepacket diffraction in space and time is investigated numerically and analytically, for a one-dimensional array of equally spaced finite-depth wells. Theoretical predictions for the lattice at long times and at low…
We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at…
Modular variables serve as a striking example of quantum nonlocality, particularly in superpositions of wave packets that are spatially well separated, where the relative phase between components cannot be accessed through conventional…
Wave functions and energies are constructed in a short-range Poeschl-Teller well (= negative quadratic secans hyperbolicus) with a quartic perturbation. Within the framework of an innovated, Lanczos-inspired perturbation theory we show that…
We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…
The scattering of wavepackets with arbitrary energy dispersion on surfaces has been analyzed. Expanding up to second order in scattering shifts, it is found that besides the known Goos-H\"anchen or Imbert-Fedorov spatial offset, as well as…
We present precise expressions of the spatial and angular Goos-Haenchen and Imbert-Fedorov shifts experienced by a longitudinally and transversally limited beam of light (wave packet) upon reflection from a dielectric interface, as opposed…
A construction of node-less atomic orbitals and energy-dependent, node-reduced partial waves is presented, that contains the full information of the atomic eigenstates and that allows to represent the scattering properties in a transparent…
We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part…
We show that Wronskians between properly chosen linearly independent solutions of the Schr\"odinger equation greatly facilitate the study of quantum scattering in one dimension. They enable one to obtain the necessary relationships between…
This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…
Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave…
There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…
We identify a class of potentials for which the scattering of flat-top solitons and thin-top solitons of the nonlinear Schr\"odinger equation with dual nonlinearity can be reflectionless. The scattering is characterized by sharp resonances…