相关论文: Special functions, raising and lowering operators

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

We survey results that have been obtained for self-adjoint operators, and especially Schr\"odinger operators, associated with mathematical models of quasicrystals. After presenting general results that hold in arbitrary dimensions, we focus…

Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…

A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…

We outline a general method for obtaining exact solutions of Schr\"{o}dinger equations with a position dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that…

Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…

The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside…

We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases…

The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…

Two families of quasi exactly solvable 2*2 matrix Schroedinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalisation of the scalar…

We present some properties of the first and second order Beltrami differential operators in metric spaces. We also solve the Schroedinger's equation for a wide class of potentials and describe spaces that the Hamiltonian of a system…

We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…

In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…

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…

We give an explicit correspondence between the domains of the self-adjoint extensions of a one-dimensional Schr\"odinger differential operator with symmetric real-valued potential and the boundary conditions the functions in the resulting…

We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…

The generalization of the factorization method performed by Mielnik [J. Math. Phys. {\bf 25}, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to…

In this paper we point out an connection between eigenfunctions of one-dimensional Schrodinger operator with polynomial potentials of degree 3, 4 and eigenfunctions of rank two commuting ordinary differential operators.

A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…