<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Ce</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>129</mml:mn><mml:mo>–</mml:mo><mml:mn>133</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>isotopes in interacting-boson-plus-fermion model

Chiang, H. C.; Hsieh, S. T.

doi:10.1103/physrevc.43.2445

Cited by 10 publications

(15 citation statements)

References 13 publications

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“…In [13] it was also shown that the quasi-exact solvability of Eqs. (12) and (13) is not due to the sl(2) Lie-algebra, which is responsible for the quasi-exact solvability of most onedimensional and effectively one-dimensional systems.…”

Section: The Dirac Equationmentioning

confidence: 99%

“…(12), and hence is also QES. In [13] it was shown that Eq. (12) and (13) gave the same QES spectrum when…”

Section: The Dirac Equationmentioning

confidence: 99%

“…The corresponding value of the magnetic field B is then obtainable from the expression l B = Zα/[(E + m)x 0 ]. Solution of ǫ and x 0 is achieved in [13] by means of the Bethe ansatz equations. There it was shown that Eq.…”

Section: The Dirac Equationmentioning

confidence: 99%

“…Later, several physical QES models were discovered, which include the two-dimensional Schrödinger [10], the Klein-Gordon [11], and the Dirac equation [12,13] of an electron moving in an attractive/repulsive Coulomb field and a homogeneous magnetic field. More recently, the Pauli and the Dirac equation minimally coupled to magnetic fields [14], and Dirac equation of neutral particles with non-minimal electromagnetic couplings [15] were also shown to be QES.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Chiang¹,

2005

Mod. Phys. Lett. A

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The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems.This model, however, does not belong to the classes based on the algebra sl(2) which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly solvable differential equation possesses a hidden osp(2, 2) superalgebra. PACS: 03.65. Pm, 31.30.Jv, 03.65.Fd

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Section: The Dirac Equationmentioning

confidence: 99%

“…(12), and hence is also QES. In [13] it was shown that Eq. (12) and (13) gave the same QES spectrum when…”

Section: The Dirac Equationmentioning

confidence: 99%

Section: The Dirac Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Chiang¹,

2005

Mod. Phys. Lett. A

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“…The parametersb 0 , c 1 are given by, 32) and the coupling constants α i and c 2 (M, N ) are defined by,…”

Section: G Case Vmentioning

confidence: 99%

Corrigendum to “sl(M+1) construction of quasi-solvable quantum M-body systems” [Ann. Phys. 309 (2004) 239–280]

Tanaka¹

2005

Annals of Physics

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We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of sl(M +1) naturally emerges. The procedure to solve the canonical-form condition for the two-body problem is presented in detail. It is shown that the resulting two-body quasi-solvable model can be uniquely generalized to the M -body system for arbitrary M under the consideration of the GL(2, K) symmetry. An intimate relation between quantum solvability and supersymmetry is found. With the aid of the GL(2, K) symmetry, we classify the obtained quasi-solvable quantum many-body systems. It turns out that there are essentially five inequivalent models of Inozemtsev type. Furthermore, we discuss the possibility of including M -body (M ≥ 3) interaction terms without destroying the quasi-solvability.

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Additional constraints on quasi-exactly solvable systems

Klishevich

2007

Theor Math Phys

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In this paper we discuss constraints on two-dimensional quantum-mechanical systems living in domains with boundaries. The constrains result from the requirement of hermicity of corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems and applying such constraints show that in real the systems are quasi-exactly solvable at best. Nevertheless in the context of pseudo-Hermitian Hamiltonians some of the constructed families are exactly solvable. *

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Ce129–133isotopes in interacting-boson-plus-fermion model

Cited by 10 publications

References 13 publications

Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Quasi-Exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Corrigendum to “sl(M+1) construction of quasi-solvable quantum M-body systems” [Ann. Phys. 309 (2004) 239–280]

Additional constraints on quasi-exactly solvable systems

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