Related papers: Scattering and bound states by localized potential…
Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the…
Quantum-mechanical scattering states are energy eigenstates obeying particular boundary conditions, whose behavior at infinity encodes the S-matrix which defines the outcoming of scattering experiments. With an eye toward numerical…
Bound states arise in many interactions among elementary field states, and are represented by poles in the scattering matrix. The emergent nature of bound states suggests that they play a perhaps under-appreciated role in specifying the…
We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.
We provide a theoretical framework to describe the interaction of a propagating guided matter wave with a localized potential in terms of quantum scattering in a confined environment. We analyze how this scattering correlates the…
In this paper we derive a formula for the density of states in the presence of inelastic scattering in the quantum well of a double barrier structure as a function of a characteristic time of the motion of electrons (namely, the round trip…
The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively. Bound states give rise to S-matrix poles, and other poles correspond to non-normalizable anti-bound, resonance and…
The Parity-Time ($\mathcal{PT}$) symmetric potentials are derived by non-Hermitian supersymmetric quantum mechanics for square well and barrier. These $\mathcal{PT}$-supersymmetric square well and barrier. The partners have complex…
We construct families of squeezed quantum states on an interval (depending on boundary conditions, we interpret the interval as a circle or as the infinite square potential well) and obtain estimates of position and momentum dispersions for…
We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the…
I propose a time-symmetric generalization of quantum mechanics that is inspired by scattering theory. The model postulates two interacting quantum states, one traveling forward in time and one backward in time. The interaction is modeled by…
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…
We develop a perturbative approach that allows one to study the surface scattering in quasi-1D waveguides with rough boundaries. Our approach is based on the construction of an effective ``bulk'' potential of a very complicated structure.…
Quantum mechanics in a one--parameter family of volcano potentials is investigated. After a discussion on their construction and classical mechanics, we obtain exact, normalisable bound states for specific values of the energy. The nature…
We consider bound and scattering states of the one-dimensional dimer formed by two coupled non-identical atoms when one of them also interacts with the zero-range potential located at the origin. By calculating the dimer localized and…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…