相关论文: Quasi exactly solvable (QES) equations with multip…

In the current paper we study extremal semilattices with respect to their equational properties. In the class $\mathbf{S}_n$ of all semilattices of order $n$ we find semilattices which have maximal (minimal) number of consistent equations.…

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This…

For quasiexactly solvable (QES) potentials a certain number of wave functions and energy levels can be analytically calculated. The complexity of an explicit calculation of the energy levels grows with the dimension of the QES sector. For a…

A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of…

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…

There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…

We study the global solution curves, and prove the existence of infinitely many positive solutions for three classes of self-similar equations, with $p$-Laplace operator. In case $p=2$, these are well-known problems involving the Gelfand…

The goal of this work is to study the existence of quasi-periodic solutions in time to nonlinear beam equations with a multiplicative potential. The nonlinearities are required to only finitely differentiable and the frequency is along a…

The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious…

For the displaced harmonic double-well oscillator the existence of exact polynomial bound states at certain displacements $d\,$ is revealed. The $N-$plets of these quasi-exactly solvable (QES) states are constructed in closed form. For…

Let K be a simple and simply connected compact Lie group. We call a (twisted) quasi-Hamiltonian K-manifold M a quasi-Hamiltonian model space if it is multiplicity free and its momentum map is surjective. We explicitly identify the subgroups…

Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…

We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami…

This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2)…

A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…

We reconsider the quasi exactly solvable matrix models constructed recently by R. Zhdanov. The 2$\times$2 matrix operators representing the algebra sl(2) are generalized to matrices of arbitrary dimension and a similar construction is…

Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…

Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…