Related papers: Compact submanifolds supporting singular interacti…
We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit…
We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional…
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…
We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this…
It has been shown recently that a nonrelativistic quantum particle constrained to a hard-wall layer of constant width built over a geodesically complete simply connected noncompact curved surface can have bound states provided the surface…
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
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…
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…
We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the particles in $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
The Salpeter equation, a standard tool in hadron physics, constitutes a well-defined three-dimensional approximation to the Bethe-Salpeter formalism for the description of bound states within quantum field theories. However, if confinement…
The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
For several embedded surfaces with zero self-intersection number in 4-manifolds, we show that an adjunction-type genus bound holds for at least one of the surfaces under certain conditions. For example, we derive certain adjunction…
Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine…
We introduce a novel concept of surface bound states in the continuum, i.e. surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
In this paper, we proved the quantum layer over a surface which is ruled outside a compact set, asymptotically flat but not totally geodesic admits ground states.
A study of the integrability of one-dimensional quantum mechanical many-body systems with general point interactions and boundary conditions describing the interactions which can be independent or dependent on the spin states of the…