An approach to one-dimensional elliptic quasi-exactly solvable models

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

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INVESTIGATION OF EXCITATION SPECTRA OF EXACTLY SOLVABLE MODELS USING INVERSION RELATIONS

International Journal of Modern Physics B ◽

10.1142/s0217979290000401 ◽

1990 ◽

Vol 04 (05) ◽

pp. 871-893 ◽

Cited By ~ 28

Author(s):

A. KLÜMPER

Keyword(s):

Solution Procedure ◽

Exactly Solvable Models ◽

Solvable Models ◽

Excitation Spectra ◽

One Dimensional ◽

Exactly Solvable ◽

State Models ◽

Set Up ◽

Quantum Antiferromagnet ◽

Inversion Relations

We study the excitations of two-dimensional classical vertex models and related one-dimensional quantum Hamiltonians. The main mathematical means we use are functional equations which are set up and solved for the excitation functions. The method is first applied to the eight-vertex model as a prototype and compared with the traditional solution procedure of the Bethe Ansatz. In the last part we investigate some q-state models, notably the biquadratic spin-1 quantum antiferromagnet and its generalizations, which recently attracted interest due to Haldane’s conjecture.

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A class of exactly solvable models for the Schrödinger equation

Open Physics ◽

10.2478/s11534-013-0301-6 ◽

2013 ◽

Vol 11 (8) ◽

Cited By ~ 4

Author(s):

Charles Downing

Keyword(s):

Differential Equation ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Mathematical Physics ◽

Transcendental Equation ◽

Exactly Solvable Models ◽

Solvable Models ◽

One Dimensional ◽

Exactly Solvable ◽

The One

AbstractWe present a class of confining potentials which allow one to reduce the one-dimensional Schrödinger equation to a named equation of mathematical physics, namely either Bessel’s or Whittaker’s differential equation. In all cases, we provide closed form expressions for both the symmetric and antisymmetric wavefunction solutions, each along with an associated transcendental equation for allowed eigenvalues. The class of potentials considered contains an example of both cusp-like single wells and a double-well.

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Generalized Generalized Spin Models Associated with Exactly Solvable Models

Progress in Algebraic Combinatorics ◽

10.2969/aspm/02410081 ◽

2018 ◽

Author(s):

Tetsuo Deguchi

Keyword(s):

Exactly Solvable Models ◽

Solvable Models ◽

Spin Models ◽

Exactly Solvable

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Interaction between Different Kinds of Quantum Phase Transitions

Quantum Reports ◽

10.3390/quantum3020015 ◽

2021 ◽

Vol 3 (2) ◽

pp. 253-261

Author(s):

Angel Ricardo Plastino ◽

Gustavo Luis Ferri ◽

Angelo Plastino

Keyword(s):

Phase Transitions ◽

Nuclear Physics ◽

Body Problem ◽

Quantum Phase Transitions ◽

Quantum Phase ◽

Exactly Solvable Models ◽

Solvable Models ◽

Many Body ◽

Pairing Interaction ◽

Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

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