Related papers: Exactly solvable potentials with finitely many dis…
The zeros of the eigenfunctions of self-adjoint Sturm-Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm-Liouville problem associated with the Schrodinger equation for…
The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be…
Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the…
Discrete integrable equations over finite fields are investigated. The indeterminacy of the equation is resolved by treating it over a field of rational functions instead of the finite field itself. The main discussion concerns a…
We introduce a new concept of infinite quasi-exactly solvable models which are constructable through multi-parameter deformations of known exactly solvable ones. The spectral problem for these models admits exact solutions for infinitely…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
Infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states are constructed in a deformed supersymmetric background. The starting points consist in one- and…
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for…
Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In this letter we derive infinitely many conserved quantities…
A new class of quasi exactly solvable potentials with a variable mass in the Schroedinger equation is presented. We have derived a general expression for the potentials also including Natanzon confluent potentials. The general solution of…
In this paper we present a novel quasi-exactly solvable model with symmetric inverted potentials which are unbounded from below. The quasi-exactly solvable states are shown to be total transmission (or reflectionless) modes. From these…
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger…
We consider a family of extensions of the Kepler-Coulomb potential on a $d$-dimensional sphere and analyze it in a deformed supersymmetric framework, wherein the starting potential is known to exhibit a deformed shape invariance property.…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength…
It is known that every positive solution of a one-dimensional Gel'fand problem can be written explicitly. In this paper we obtain exact expressions of all the eigenvalues and eigenfunctions of the linearized eigenvalue problem at each…
Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the…