相关论文: Exact solution for two-dimensional Coulomb matrix …
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…
Closed form expressions for three-dimensional potential and force field due to singularities distributed on a finite flat surface have been used to develop a fast and accurate BEM solver. The exact expressions have been investigated in…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction…
The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim 1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
Symmetric and antisymmetric terms have been obtained in the framework of the variational approach for two-dimensional (2D) Coulomb systems of symmetric trions XXY. Stability diagrams and certain anomalies arising in the 2D space are…
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…