The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra s1(2,C) or A1. This leads to new types of both PT-symmetric and non-PT-symmetric Hamiltonians. (C) 2000 Elsevier Science B.V.

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University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Physics Letters, Section A: General, Atomic and Solid State Physics

We demonstrate that the recent paper by Abhinav and Panigrahi entitled 'Supersymmetry, PT-symmetry and spectral bifurcation' [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex sl(2) potential algebra. © 2010 Elsevier Inc.

Annals of Physics

Comment on 'Supersymmetry, PT-symmetry and spectral bifurcation'

The PT-symmetric complexi?ed Scarf II potential V(x) =-V 1sech2 x + iV2sechx tanh x, V1 &gt; 0, V2 ≠= 0, is revisited to study the interplay among its coupling parameters. The existence of an isolated real and positive energy level that has recently been identfied as a spectral singularity or zero-width resonance is here demonstrated through the behaviour of the corresponding wavefunctions and some property of the associated pseudo-norms is pointed out. We also construct four different rationally extended supersymmetric partners to V(x), which are PT-symmetric or complex non-PT-symmetric according to the coupling parameters range. A detailed study of one of these partners reveals that SUSY preserves the V(x) spectral singularity existence. © 2010 IOP Publishing Ltd.

Journal of Physics A: Mathematical and Theoretical

An update on the PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally extended supersymmetric partners

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of -symmetric Hamiltonians. The method is applied to the Hermitian analogue of the -symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a -symmetric extension of the one-parameter trigonometric Pöschl-Teller potential. © 2006 IOP Publishing Ltd.

Journal of Physics A: Mathematical and General

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

The simplest purely imaginary and piecewise constant PT-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete. We interpret such a model as an initial element of the generalized non-Hermitian Witten's hierarchy of solvable Hamiltonians and construct its first supersymmetric partner in closed form. © World Scientific Publishing Company.

International Journal of Modern Physics A

PT-symmetric supersymmetry in a solvable short-range model

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model. © 2005 IOP Publishing Ltd.

Pseudo-Hermiticity and some consequences of a generalized quantum condition

The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that under supersymmetric transformations the underlying potential picks up a reflectionless part. (C) 2000 Elsevier Science B.V.

PT-symmetric sextic potentials

We construct an isospectrum system in terms of a real and a complex potential to show that the underlying PT-symmetric complex Hamiltonian possesses a real spectrum which is shared by its real partner.

Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Publisher	-
ISSN	0375-9601
Open Access	Yes