Existence of different intermediate Hamiltonians in type A 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" display="inline" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi></mml:math>-fold supersymmetry II

Bagchi, B.; Tanaka, Toshiaki

doi:10.1016/j.aop.2010.02.018

Annals of Physics

2010

DOI: 10.1016/j.aop.2010.02.018

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Existence of different intermediate Hamiltonians in type A N-fold supersymmetry II

B. Bagchi¹,

Toshiaki Tanaka²

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Cited by 6 publications

References 19 publications

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Type B 3-fold supersymmetry and non-polynomial invariant subspaces

Tanaka

2013

Journal of Mathematical Physics

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We obtain the most general type B 3-fold supersymmetry by solving directly the intertwining relation. We then show that it is a necessary and sufficient condition for a second-order linear differential operator to have three linearly independent local analytic solutions. We find that there are eight linearly independent non-trivial linear differential operators of this kind. As a by-product, we find new quasi-solvable second-order operators preserving a monomial or polynomial subspace, one in type B, two in type C, and four in type X 2 , all of which have been missed in the existing literature. In addition, we show that type A, type B, and type C 3-fold supersymmetries are connected continuously via one parameter. A few new quasi-solvable models are also presented. C 2013 AIP Publishing LLC. [http://dx.

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Type B 3-fold supersymmetry and non-polynomial invariant subspaces

Tanaka

2013

Journal of Mathematical Physics

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$GL(3,\mathbb {C})$ G L ( 3 , C ) invariance of type B 3-fold supersymmetric systems

Tanaka

2014

Journal of Mathematical Physics

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Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under G L(3, C) homogeneous linear transformations. In particular, we prove explicitly that the parameter space is transformed as an adjoint representation of it and that every coefficient of the characteristic polynomial appeared in 3-fold superalgebra is algebraic invariants. In the type A case, it includes as a subgroup the G L(2, C) projective transformation studied in the literature. We argue that any N -fold supersymmetric system has a G L(N , C) invariance for an arbitrary integral N . C 2014 AIP Publishing LLC.

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Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics

Quesne¹

2012

J. Phys.: Conf. Ser.

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In recent years, one of the most interesting developments in quantum mechanics has been the construction of new exactly solvable potentials connected with the appearance of families of exceptional orthogonal polynomials (EOP) in mathematical physics. In contrast with families of (Jacobi, Laguerre and Hermite) classical orthogonal polynomials, which start with a constant, the EOP families begin with some polynomial of degree greater than or equal to one, but still form complete, orthogonal sets with respect to some positive-definite measure. We show how they may appear in the bound-state wavefunctions of some rational extensions of well-known exactly solvable quantum potentials. Such rational extensions are most easily constructed in the framework of supersymmetric quantum mechanics (SUSYQM), where they give rise to a new class of translationally shape invariant potentials. We review the most recent results in this field, which use higher-order SUSYQM. We also comment on some recent re-examinations of the shape invariance condition, which are independent of the EOP construction problem.

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Existence of different intermediate Hamiltonians in type A N-fold supersymmetry II

Cited by 6 publications

References 19 publications

Type B 3-fold supersymmetry and non-polynomial invariant subspaces

Type B 3-fold supersymmetry and non-polynomial invariant subspaces

$GL(3,\mathbb {C})$ G L ( 3 , C ) invariance of type B 3-fold supersymmetric systems

Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics

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