Related papers: Particle in a box with a delta-function potential:…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…
We study the behavior of a quantum particle, trapped in localized potential, when the trapping potential starts suddenly to move with constant velocity. In one dimension we have reproduced the results obtained by Granot and Marchewka, Ref.…
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron-positron plasmas, for a wide range of…
Adopting hyperon-nucleon and hyperon-nucleon-nucleon interactions parametrized in chiral effective field theory, single-particle potentials of the $\Lambda$ and $\Sigma$ hyperons are evaluated in symmetric nuclear matter and in pure neutron…
We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such Hamiltonian converges…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for…
We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and…
The one-dimensional Schr\"odinger equation with the point potential in the form of the derivative of Dirac's delta function, $\lambda \delta'(x)$ with $\lambda$ being a coupling constant, is investigated. This equation is known to require…
We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits…
We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk,…
We extend the microscopic particle-rotor model for hypernuclear low-lying states by including the derivative and tensor coupling terms in the point-coupling nucleon-$\Lambda$ particle ($N\Lambda$) interaction. Taking $^{13}_{~\Lambda}$C as…
We consider three one dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.
In this paper we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to…
The Fredholm equations for one-dimensional two-component Fermions with repulsive and with attractive delta-function interactions are solved by an asymptotic expansion for A) strong repulsion, B) weak repulsion, C) weak attraction and D)…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
Starting from a continuum theory of defects, that is the analogous to three-dimensional Einstein-Cartan-Sciama-Kibble gravity, we consider a charged particle with spin 1/2 propagating in a uniform magnetic field coincident with a wedge…
We present a quantum theory for the interaction of a two level emitter with surface plasmon polaritons confined in single-mode waveguide resonators. Based on the Green's function approach, we develop the conditions for the weak and strong…
The solution of the Dirac equation for an attractive linear potential is considered. The Lorentz nature of the potential (vector or scalar) affects the existence of bound states. For simplicity, and since it is sufficient for the goals of…
In scattering by singular potentials $g^2U(s;r)$, the coupling constant $g^2$ is continuously decreased to zero while the stage $s$ of singularity raised simultaneously beyond all limits by some functional relation $F(g^2;s)=0$. In the…