相关论文: Unusual bound or localized states
We study charged particles in three dimensions interacting via a short-range potential in addition to the Coulomb potential. When the Bohr radius and the scattering length are much larger than the potential range, low-energy physics of the…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
We discuss the arising of bound states solutions of the Schr\"odinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we…
In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
We study the third quantization of the Friedmann-Robertson-Walker cosmology with $N$-minimal massless fields. The third quantized Hamiltonian for the WDW equation in the minisuperspace consists of infinite number of intrinsic…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole…
We explore quantum localization phenomena in a system of two coupled tight-binding chains with incommensurate periods. Employing the inverse participation ratio as a measure of localization, we investigate the effects of geometric…
On a simple model $V(x,y)=A\,x^2+B\,y^2+C\,x^2y^2+D\,(x^2y^4+x^4y^2)$ we demonstrate that even in a classically repulsive regime (i.e., at couplings which make the potential decreasing to $-\infty$ in some directions) quantum mechanics may…
We present a quantum localization phenomenon that exists in periodically kicked 3D rotors, but is absent in the commonly studied 2D ones: edge localization. We show that under the condition of a fractional quantum resonance there are states…
The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordstr\"{o}m, Kerr and Kerr-Newman fields. The behavior of effective potentials in the…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
We propose a general method that allows to detect the existence of normalizable ground states in supersymmetric quantum mechanical systems with non-Fredholm spectrum. We apply our method to show the existence of bound states at threshold in…
In this work we propose an alternative description of the quantum mechanics of a massive and spinning free particle in anti-de~Sitter spacetime, using a phase space rather than a spacetime representation. The regularizing character of the…
We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a…