Related papers: Analytically Solvable 2D Potentials: Bound States
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…
Within the formalism of relativistic quantum field theory an adequate framework for the description of two-particle bound states, such as, for instance, all conventional (i.e., non-exotic) mesons, is provided by the Poincar\'e-covariant…
General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A…
We show that the two-dimensional (2D) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete. We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and…
In the article the Fourier series analytical solutions of uniformly loaded rectangular thin plates with symmetrical boundary conditions are considered. For all the cases the numerical values are tabulated.
Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…
Translationally invariant symmetric polynomials as coordinates for $N$-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland $N$-body Hamiltonians, after appropriate gauge…
Associated Lam\'e potentials $V(x)=a(a+1)m\sn^2(x,m)+b(b+1)m{\cn^2 (x,m)}/{\dn^2(x,m)}$ are used to construct complex, PT-invariant, periodic potentials using the anti-isospectral transformation $x \to ix+\beta$, where $\beta$ is any…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension)…
In this work, the analytical solution of the hyper-radial Schr\"{o}dinger equation for the spherical Woods-Saxon potential in D dimensions is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris…
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of…
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…
Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues are considered. The method of evaluation of quantities $\sigma_n$ known as the singular values of $H$ is proposed. Its basic…
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of…