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May 30, 2017 in this article we study numerically and theoretically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic.
(1994), quasi-exactly solvable models in quantum mechanics, bristol: institute of physics publishing, isbn 0-7503-0266-6, mr 1329549; external links.
An efficient procedure for constructing quasi-exactly solvable matrix models is suggested. It is based on the fact that the representation spaces of representations.
Another direction of investigation of quasi-exactly solvable schrödinger is the study of time-dependent hamiltonian.
Jul 18, 2017 the exact solution of the schrödinger equation for the four quasi-exactly solvable potentials is presented using the functional bethe ansatz.
A simple recipe to construct exactly and quasi-exactly solvable (qes) hamiltonians in one-dimensional ‘discrete’ quantum mechanics is presented. It reproduces all the known hamiltonians whose eigenfunctions consist of the askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable.
Highlights the quasi-exactly solvable treatments of a class of singular anharmonic models. Exact solutions to a class of integer power singular potential. Solutions obtained in terms of the roots to the bethe ansatz equations. Results useful in describing diatomic molecules and elastic differential cross sections for high energy scattering.
A v turbiner 1988 quasi-exactly-solvable problems and sl(2) algebra. A g ushveridze 1994 quasi-exactly solvable models in quantum mechanics.
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known two-dimensional lie-algebraic quasi-exactly solvable system based on lie algebra su(3).
During the last decades, an intermediate class between the es models and the non-solvable models was introduced for which a finite part of the spectrum can be determined by purely algebraic means. For this reason, they were named quasi-exactly solvable (qes) models [9–14].
And show that the action of the hamiltonian in these common eigenspaces can be represented by a quasi-exactly solvable reduced hamiltonian.
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 property. These models have the notable feature that they do not preserve u(1) symmetry, which is typically associated with a non-conservation of particle number.
The class of quasi-exactly-solvable problems in ordinary quantum mechanics discovered recently shows remarkable parallels with rational two-dimensional conformal field theories. This fact suggests that investigation of the quasi-exactly-solvable models may shed light on rational conformal field theories.
A/prof yao-zhong zhang's research interests are in: lie (super)algebras, quantized algebras, representations, quantum integrable systems, (quasi-)exactly solvable models, correlation functions, supersymmetry and conformal field theory. Yao-zhong zhang received his phd from northwest university, china, in 1988 under the supervision of prof bo-yu.
Quasi-exactly solvable (qes) models (whose hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although qes models are a recent discovery, the results are already numerous.
Supersymmetry (susy) in quantum mechanics is extended from square integrable states to those satisfying the outgoing wave boundary condition.
A new two-parameter family of quasi-exactly solvable quartic polynomial potentials is introduced. Heretofore, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial potential is sextic. This belief is based on the assumption that the hamiltonian must be hermitian.
Feb 27, 2020 the equation of the γ-unstable bohr hamiltonian, with particular forms of the sextic potential in the β shape variable, is exactly solved for a finite.
An efficient procedure for constructing quasi-exactly solvable matrix models is suggested. It is based on the fact that the representation spaces of representations of the algebra sl(2, r) within the class of first-order matrix differential operators contain finite dimensional invariant subspaces.
The aim of the present paper is to describe the quasi-exactly solvable random matrix models associated with some of the simplest quasi-exactly solvable quantum mechanical problems.
In this case, the operator l is called a g-lie-algebraic quasi-exactly-solvable operator. Usually, one can indicate basis where l has block-triangular form.
Is the same as factorization in quasi-exactly solvable models [11,13]. [13], some one-dimensional quasi-exactly solvable models have been ob-tained using the generalized master function approach. As far as elliptic quasi-exactly solvable potentials are concerned, these models have not been investigated, using this method.
Quasi-exactly solvable (qes) models (whose hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical.
A differential operator h is called quasi-exactly solvable if it lies in the universal enveloping algebra of a quasi-exactly solvable lie algebra of differential operators.
Sep 12, 2014 the quasi-spin algebra associated with the hamiltonian (19) is so(5) and makes the problem analytically solvable (hecht, 1965).
This basic equation is quasi-exactly solvable for certain values of its parameters and exact solutions are given by polynomials of degree n in t with n being non-negative integers. In fact, the above equation is a special case of the general second order differential equations solved in [26] by means of the bethe ansatz method.
Potential with n-dependent coupling, forms a quasi-exactly solvable model. Making a polynomial ansatz for the closed-form eigenfunctions, we obtain a three-term recursion relation, from which the known energies are derived and the polynomial coefficients are factorized.
Important for higher dimensional quasi-exactly solvable problems, because as we shall see, for the case of one (real or complex) variable, all the quasi-exactly solvable systems arise from the above sl(2) representation. Quasi-exact solvability the idea behind the phenomenon of quasi-exact solvability [17] is that there.
One-dimensional quasi-exactly solvable differential equations and their re- exactly solvable and unsolvable models in the sense that exact solution in an alge-.
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still incomplete) sets of exact (algebraic) solutions.
We suggest a systematic method of extension of quasiexactly solvable (qes) systems. We construct finite-dimensional subspaces on the basis of special functions (hypergeometric, airy, bessel ones) invariant with respect to the action of differential operators of the second order with polynomial coefficients. As an example of physical applications, we show that the known two-photon rabi.
Abstract in this article we study numerically and theoretically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic.
Various quasi-exact solvability conditions, involving the parameters of the periodic associated lamé potential, are shown to emerge naturally in the quantum hamilton–jacobi (qhj) approach. We study the singularity structure of the quantum momentum function, which yields the band-edge eigenvalues and eigenfunctions and compare it with the solvable and quasi-exactly solvable non-periodic.
Nodal surfaces in quasi-exactly solvable models pierre-fran˘cois loos, 1peter gill, and dario bressanini2 1research school of chemistry, australian national university, canberra, australia 2dipartimento di scienza e alta tecnologia, universit a dell’insubria, como, italy 16th conference in computational and mathematical.
Several quasi-exactly solvable models of few-particle systems are discussed. In particular, the hooke atom (also known as harmonium) and its extensions appropriate to a description of non-born.
We establish a direct connection between inhomogeneous xx spin chains (or free fermion systems with nearest-neighbors hopping) and certain qes models on the line giving rise to a family of weakly orthogonal polynomials. We classify all such models and their associated xx chains, which include two families related to the lamé (finite gap) quantum potential on the line.
This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources.
We construct a new example of 2 × 2-matrix quasi-exactly solvable (qes) hamiltonian which is associated to a potential depending on the jacobi elliptic functions. We establish three necessary and sufficient algebraic conditions for the previous operator to have an invariant vector space whose generic elements are polynomials.
Was found [3] that the calogero model is characterized by the hidden algebra sl nand that the calogero hamiltonian (1) is a lie-algebraic, exactly-solvable operator. The goal of this letter is to show that the calogero hamiltonian can be generalized to a lie-algebraic,quasi-exactly-solvable operator leading.
For each model, we construct a complete set of commuting integrals of motion of the hamiltonian, fully characterize the common eigenspaces of the integrals of motion and show that the action of the hamiltonian on these common eigenspaces can be represented by a quasiexactly solvable reduced hamiltonian, whose expression in terms of the usual.
Keywords: duality, quasi-exactly solvable models, ricatti equation, exact wkb (some figures may appear in colour only in the online journal) preamble the concept of duality is widely used in modern physics [1–6]. Establishing of connections between different regimes of a system (or between different systems) often yields novel.
May 16, 2017 quasimode computation in structures including several dispersive materials. Guillaume demésy, mauricio garcia-vergara, frédéric zolla,.
A few quasi-exactly solvable models are studied within the quantum hamilton-jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition for quasi-exact solvability.
Abstract: we present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively.
A novel quasi-exactly solvable model with total transmission modes hing-tong cho and choon-lin ho open abstract view article a novel quasi-exactly solvable model with total transmission modes pdf a novel quasi-exactly solvable model with total transmission modes.
Ushveridze, quasi-exactly solvable models in quantum mechanics, (iopp, bristol, 1994). Turbiner, quasi-exactly-solvable problems and sl(2) algebra.
A new method of constructing multi-dimensional quasi-exactly solvable models of quantum mechanics is proposed.
Focus on a relatively new method which leads to quasi–exactly solvable models. During the preparation of the work it proved to be very convenient, both for the author and – i hope – for the readers, to gather the mathematical definitions and the most fundamental facts concerning the group theory in a separate, preliminary chapter.
For each model, we construct a complete set of commuting integrals of motion of the hamiltonian, fully characterize the common eigenspaces of the integrals of motion, and show that the action of the hamiltonian in these common eigenspaces can be represented by a quasi-exactly solvable reduced hamiltonian, whose expression in terms of the usual.
Abstract: a few quasi-exactly solvable models are studied within the quantum hamilton-jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition for quasi-exact solvability.
A generalization of the procedures for constructing quasi-exactly solvable models with one degree of freedom to (quasi-)exactly solvable models of n particles on a line allows deriving many well-known models in the framework of a new approach that does not use root systems.
The quasi–exact solvability arises as an effect of relation between the potential system and a spin system with the total spin s, resulting in 2s+1 exactly known.
Parafermions are emergent excitations that generalize majorana fermions and can also realize topological order. In this letter, we present a nontrivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave functions, which are matrix-product states and have a particularly elegant interpretation in terms of fock.
Although qes models are a recent discovery, the results are already numerous. Collecting the results of qes models in a unified and accessible form, quasi-exactly solvable models in quantum mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations.
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