Related papers: Explicit Bound States for Certain N-Body Hamiltoni…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
Physical self-adjoint extensions and their spectra of the simplest one-dimensional Hamiltonian operator in which the mass is constant except for a finite jump at one point of the real axis are correctly found. Some self-adjoint extensions…
Even a first approximation of bound states requires contributions of all powers in the coupling. This means that the concept of "lowest order bound state" needs to be defined. In these lectures I discuss the "Born" (no loop, lowest order in…
The effects of two distinct operations of the elements of the symmetry groups of a Hamiltonian on a quantum state might be equivalent in some specific zones of coordinate space. Making use of the matrix representations of the groups, the…
The paper studies the structure of high-order adiabatic approximation of a wave function for slowly changing Hamiltonians. A constructive technique for explicit separation of fast and slow components of the wave function is developed. The…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
Effective Hamiltonians for doubly excited Heliums states based on approximate O(4) symmetry are revised. New quantum numbers for a 4D Harmonic Oscillator are assigned to Helium states with both electrons in the n=2 shell. An effective…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground…
We investigate the formation of three-body bound states in the continuum by tracing pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a…
We consider lepton-neutron (and lepton-antineutron) bound states and resonances which appear due to spin-spin, spin-orbital interactions,neutron polarization by muon. Our analis is also true for any system which include one charge and one…
We solve a two-body problem for electrons in a one-dimensional system to show that two-electron bound states can arise as a result of the image-potential-induced spin-orbit interaction (iSOI). The iSOI contributes an attractive component to…
A bound state in the continuum (BIC) is a spatially bounded energy eigenstate lying in a continuous spectrum of extended eigenstates. While various types of single-particle BICs have been found in the literature, whether or not BICs can…
We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer…
Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of…
In this note, we present a new method to investigate the positronium states in ${\rm{QED_3}}$. According to the $\rm{K\ddot{a}ll\acute{e}n-Lehmann}$ spectral representation, the energy eigenvalues of bound states are poles of the…