Related papers: Quantum Mechanics of Multi-Prong Potentials
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…
In an N-body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials and long-range potentials, from the high-velocity limit of…
The spin of the neutron allows neutron scattering to reveal the magnetic structure and dynamics of materials over nanometre length scales and picosecond timescales. Neutron scattering is particularly in demand in order to understand…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
Using phase-equivalent supersymmetric partner potentials, a general result from the inverse problem in quantum scattering theory is illustrated, i.e., that bound-state properties cannot be extracted from the phase shifts of a single partial…
Quantum pumping holds great potential for future applications in micro- and nanotechnology. Its main feature, dissipationless charge transport, is theoretically possible via several different mechanisms. However, since no unambiguous…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in…
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are…
We investigate non-relativistic quantum mechanical potentials between fermions generated by various classes of QFT operators and evaluate their singularity structure. These potentials can be generated either by four-fermion operators or by…
We consider a minisuperspace model for a closed universe with small and positive cosmological constant, filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a…
In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the…
We calculate the quantum states of regular polygons made of 1D quantum wires treating each polygon vertex as a scatterer. The vertex scattering matrix is analytically obtained from the model of a circular bend of a given angle of a 2D…
It is well known that string theory generates the idea of higher dimensional spacetime instead of the (3+1) dimensions, in which we seem to live. It indicates that the extra space dimensions may remain curled up into very small space. In…
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…