Existence of different intermediate Hamiltonians in type A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" display="inline" overflow="scroll"><mml:mrow><mml:mi mathvariant="script">N</mml:mi></mml:mrow></mml:math>-fold supersymmetry

Bagchi, B.; Tanaka, Toshiaki

doi:10.1016/j.aop.2009.08.002

Cited by 12 publications

(4 citation statements)

References 31 publications

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“…This is another example of the possible existence of different intermediate Hamiltonians in higher-order SUSYQM [27] or in type A N -fold supersymmetry [41].…”

Section: Partner Of Rationally-extended Morse Potentials In Unbroken ...mentioning

confidence: 95%

Revisiting (Quasi-)Exactly Solvable Rational Extensions of the Morse Potential

Quesne

2012

Int. J. Mod. Phys. A

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The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials V A,B,ext (x), obtained from a conventional Morse potential V A−1,B (x) by the addition of a bound state below the spectrum of the latter, is re-obtained. More importantly, the existence of another family of extended potentials, strictly isospectral to V A+1,B (x), is pointed out for a well-chosen range of parameter values. Although not shape invariant, such extended potentials exhibit a kind of 'enlarged' shape invariance property, in the sense that their partner, obtained by translating both the parameter A and the degree m of the polynomial arising in the denominator, belongs to the same family of extended potentials. The point canonical transformation connecting the radial oscillator to the Morse potential is also applied to exactly solvable rationally-extended radial oscillator potentials to build quasi-exactly solvable rationally-extended Morse ones. Running head: Rational Extensions of Morse Potential

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“…This is another example of the possible existence of different intermediate Hamiltonians in higher-order SUSYQM [27] or in type A N -fold supersymmetry [41].…”

Section: Partner Of Rationally-extended Morse Potentials In Unbroken ...mentioning

confidence: 95%

Revisiting (Quasi-)Exactly Solvable Rational Extensions of the Morse Potential

Quesne

2012

Int. J. Mod. Phys. A

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“…The existence of different intermediate Hamiltonians, as observed in the PSUSY approach of Sec. 3, is also worth analyzing along the lines of type A N -fold supersymmetry [31,33].…”

Section: Final Commentsmentioning

confidence: 99%

Higher-Order Susy, Exactly Solvable Potentials, and Exceptional Orthogonal Polynomials

Quesne

2011

Mod. Phys. Lett. A

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Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of kth-order supersymmetric quantum mechanics, with special emphasis on k = 2. It is shown that for µ = 1, 2, and 3, there exist exactly µ distinct potentials of µth type and associated families of exceptional orthogonal polynomials, where µ denotes the degree of the polynomial g µ arising in the denominator of the potentials.Running head: Higher-order SUSY

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“…The inclusion of a position-dependent effective mass in the latter has been dealt with [49], as well as the replacement of the real potential by a complex one, either PT -symmetric or not [19,50]. The EOP have been studied in the framework of the quantum Hamilton-Jacobi formalism in connection with the supersymmetric WKB quantization condition [51] and in that of type A N -fold supersymmetry and quasi-solvability [52,53,54]. They have also been shown to be useful in the context of the Dirac equation coupled minimally or non-minimally with some external field and in that of the Fokker-Planck equation [55].…”

Section: Final Commentsmentioning

confidence: 99%

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

Cited by 12 publications

References 31 publications

Revisiting (Quasi-)Exactly Solvable Rational Extensions of the Morse Potential

Revisiting (Quasi-)Exactly Solvable Rational Extensions of the Morse Potential

Higher-Order Susy, Exactly Solvable Potentials, and Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics

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