Related papers: Barrier-bound States in Flat-band Systems
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
A simple analytical expression for the electric dipole polarizability of the three-hadron bound system having only one stable bound state has been derived neglecting by the higher orbital components of the off-shell three-body transition…
We have studied the bound states of the extra electron in a molecular wire, corresponding to the physical situation of the electron tunneling through the wire. Based on formalism of the scattering operator that accounts for many-electron…
Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state…
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the ionization threshold. For atomic systems at the critical…
We study the nonlinear Schr\"odinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both…
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…
Bound states in the continuum (BICs) are quantum states that remain localized despite existing within a continuum of extended, delocalized states. They defy conventional wave theories and could be instrumental for quantum technologies that…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
A theory of bipolaron states in quantum wires with a parabolic potential well is developed applying the Feynman variational principle. The basic parameters of the bipolaron ground state (the binding energy, the number of phonons in the…
One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…
The electronic states of a finite-width graphene sheet in the presence of an electrostatic confining potential and a perpendicular magnetic field are investigated. The confining potential shifts the Landau levels inside the well and creates…
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…
We modeled the electron and hole states in Si/SiO2 quantum wells within a basis of standing waves using the 30-band k.p theory. The hard-wall confinement potential is assumed, and the influence of the peculiar band structure of bulk silicon…
We perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ($^3$CH$_2$, $^2$CH$_3^{\bullet}$, $^3$O$_2$) going beyond the Born-Oppenheimer approximation and accounting for nuclear…
A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and…
On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
The conditions leading to flat dispersionless frequency bands in truly one-dimensional parity-time ($\cal PT$) symmetric metamaterials comprising split-ring resonators (SRRs) arranged in a binary pattern are obtained analytically. In this…