Related papers: Calculating resonance positions and widths using t…
Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed…
A quantum version of a recent formulation of transition state theory in {\em phase space} is presented. The theory developed provides an algorithm to compute quantum reaction rates and the associated Gamov-Siegert resonances with very high…
The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization.…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
Linear response theories in the continuum capable of describing continuum spectra and dynamical correlations are presented. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform…
The formalism of Siegert states to describe the resonant scattering in quantum theory is extended to the resonant scattering of electromagnetic waves on periodic dielectric arrays. The excitation of electromagnetic Siegert states by an…
The Rayleigh-Ritz procedure for determining bound-states of the Schr\"{o}dinger equation relies on spectral representation of the solution as a linear combination of the basis functions. Several possible extensions of the method to…
The RSE Born Approximation is a new scattering formula in Physics, it allows the calculation of strong scattering at all frequencies via the Fourier transform of the scattering potential and Resonant-states. In this paper I apply the RSE…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian…
The main motivation for this work is the exploration of rotational-vibrational states corresponding to electronic excitations in a pre-Born-Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the…
We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state…
In molecular reactions at the microscopic level the appearance of resonances has an important influence on the reactivity. It is important to predict when a bound state transitions into a resonance and how these transitions depend on…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R- matrix but rather by the equation $1- R_{nn}L_n = 0$, relating R- matrix element…
The parametric ladder climbing (successive Landau-Zener-type transitions) and the quantum saturation of the threshold for the classical parametric autoresonance due to the zero point fluctuations at low temperatures are discussed. The…
In this paper, a nice theoretical scheme is presented to investigate resonant and bound states in weakly bound nuclear systems by the use of isospectral potentials together with hyperspherical harmonics expansion. In this scheme, a new…
In quantum mechanics, the Wigner function $\rho_W(\textbf{r},\textbf{p})$ serves as a phase-space representation, capturing information about both the position $\textbf{r}$ and momentum $\textbf{p}$ of a quantum system. The Wigner function…
It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum…