相关论文: Exactly solvable associated Lame potentials and su…

We explore the effects of a strongly-coupled, approximately scale-invariant sector on the renormalization of soft supersymmetry breaking terms. A useful formalism for deriving exact results for renormalization of soft supersymmetry breaking…

We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and…

A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the finite-gap Lame equation. This gives a natural explanation for peculiar properties of the periodic quantum system underlying diverse models and…

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…

The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the…

We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged…

We treat the eigenvalue problem posed by self-similar potentials, i.e. homogeneous functions under a particular affine transformation, by means of symmetry techniques. We find that the eigenfunctions of such problems are localized, even…

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated…

We use a Lie algebraic technique to construct complex quasi exactly solvable potentials with real spectrum. In particular we obtain exact solutions of a complex sextic oscillator potential and also a complex potential belonging to the Morse…

A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…

We discuss integrating out matter fields and integrating in matter fields in four dimensional supersymmetric gauge theories. Highly nontrivial exact superpotentials can be easily obtained by starting from a known theory and integrating in…

By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…

We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…

A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…

We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric…

We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new…