Related papers: Approximate stabilization of a quantum particle in…
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to…
The nonlinear Schr\"odinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power…
We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
We solve the stationary Schr\"odinger equation for a particle confined to a 3D spherical wedge -- the region $\{(r,\theta,\phi): 0 \leq r \leq R,\, 0 \leq \theta \leq \pi,\, 0 \leq \phi \leq \Phi\}$ with Dirichlet BCs on all surfaces. This…
Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like…
We find that the double-threshold voltage-current characteristics in the insulating regime in the ultra-clean two-valley two-dimensional electron system in SiGe/Si/SiGe quantum wells are promoted by perpendicular magnetic fields, persisting…
The dynamical behavior of quantum state properties under intrinsic decoherence models can be modified by the presence of external magnetic fields. Although generically external magnetic fields are detrimental to preserve quantumness in the…
For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless…
Non-separable $D-$dimensional partial differential Schr\"{o}dinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case)…
We consider a free particle,V(r)=0, with position-dependent mass m(r)=1/(1+zeta^2*r^2)^2 in the d-dimensional schrodinger equation. The effective potential turns out to be a generalized Poschl-Teller potential that admits exact solution.
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…
This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…
Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final state interactions. A…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems…
Particle scattering and vacuum instability in a constant inhomogeneous electric field of particular peak configuration that consists of two (exponentially increasing and exponentially decreasing) independent parts are studied. It presents a…
We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the…
We study quantum effects induced by a point-like object that imposes Dirichlet boundary conditions along its world-line, on a real scalar field $\varphi$ in 1, 2 and 3 spatial dimensions. The boundary conditions result from the strong…