相关论文: A Pedestrian Introduction to Gamow Vectors
We express the resonant energies of the delta-shell potential in terms of the Lambert $W$ function, and we calculate their decay widths and decay constants. The ensuing numerical results strengthen the interpretation of such decay widths…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
Quantum scattering in the presence of a potential valley followed by a barrier is examined for the case of a Morse potential, for which exact analytic solutions to the Schr\UNICODE{0xf6}dinger equation are known in terms of confluent…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
In the framework of decay theory of Goldberger and Watson we treat $\alpha$-decay of nuclei as a transition caused by a residual interaction between the initial unperturbed bound state and the scattering states with alpha-particle. The…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave…
Exotic compact objects may resemble black holes very closely while remaining horizonless. They may be distinguished from black holes because they effectively give rise to a resonant cavity for the propagation of low frequency gravity waves.…
In this paper we show how rotational bands of resonances can be described by using trajectories of poles of the scattering amplitude in the complex angular momentum plane: each band of resonances is represented by the evolution of a single…
The possible relation of the wave nature of particles to gravitation as an emergent phenomenon is addressed. Hypothetical particles are considered as spatially confined oscillations (SCOs) and are constructed through the superposition of…
We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…
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…
We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering resonances are shown…
We study the renormalized Nelson model for a scalar matter particle in a continuous confining potential interacting with a possibly massless quantized radiation field. When the radiation field is massless we impose a mild infrared…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
Making use of the analytical properties of the $S$-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We propose a self-consistent vectorial method, based on a Green's function technique, to describe the Fano resonances that appear in guided mode resonance gratings. The model provides intuitive expressions of the reflectivity and…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…