Related papers: Solution of the Three--Anyon Problem
The spectrum of anyons confined in harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions have been shown analytically, the nonlinear dependence…
The 3-anyon problem is studied using a set of variables recently proposed in an anyon gauge analysis by Mashkevich, Myrheim, Olaussen, and Rietman (MMOR). Boundary conditions to be satisfied by the wave functions in order to render the…
We present new family of exact analytic solutions for three anyons in a harmonic potential (or in free space) in terms of generalized harmonics on $S^3$, which supplement the known solutions. The new solutions satisfy the hard-core…
The anharmonic electron-phonon problem is solved in the infinite-dimensional limit using quantum Monte Carlo simulation. Charge-density-wave order is seen to remain at half filling even though the anharmonicity removes the particle-hole…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We map the three-body problem in two dimensions onto one particle in a three dimensional potential treatable by a purposely-developed boundary-matching-matrix method. We evaluate binding energies of trions $X^{\pm}$, excitons bound by a…
Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr\"{o}dinger equation of the reflection-asymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic…
The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
The problem of three different masses bound by harmonic oscillator potentials is solved exactly. It is shown that Jacobi coordinates cannot, in general, decouple this system into two three-dimensional oscillators but this decoupling can…
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of…
We discuss the problem of N anyons in harmonic well, and derive the semi-classical spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed.
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…