We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Pöschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.

B BAGCHI

S MALLIK

C QUESNE

Fulltext

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

International Journal of Modern Physics A

This paper examines the features of a generalized position-dependent mass Hamiltonian Hm in a supersymmetric framework in which the constraints of pseudo-Hermiticity and [formula omitted] are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials [formula omitted] which are inherently [formula omitted]-symmetric. The qualitative spectral behavior of Hm is studied and several interesting consequences are noted. © 2013, American Institute of Physics. All rights reserved.

Journal of Mathematical Physics

[formula omitted]-conserved effective mass Hamiltonians through first and higher order charge operator [formula omitted] in a supersymmetric framework

This paper examines the features of a generalized position-dependent mass Hamiltonian H-m in a supersymmetric framework in which the constraints of pseudo-Hermiticity and CPT are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials W-m(x) which are inherently PT-symmetric. The qualitative spectral behavior of H-m is studied and several interesting consequences are noted. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792472]

CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework

A conditionally exactly solvable potential, the supersymmetric partner of the harmonic oscillator is investigated in the PT-symmetric setting. It is shown that a number of properties characterizing shape-invariant and Natanzon-class potentials generated by an imaginary coordinate shift x-iε also hold for this potential outside the Natanzon class. © 2004 Elsevier B.V. All rights reserved.

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

PT symmetry of a conditionally exactly solvable potential

We construct isospectral partner potentials of a complex PT-invariant potential, viz., V(x) = -V1 sech2 x-iV2 sech x tanh x using Darboux's method. One set of isospectral potentials are obtained which can be termed 'satellite potentials', in the sense that they are of the same form as the original potential. In a particular case, the supersymmetric partner potential has the same spectrum, including the zero energy ground state, a fact which cannot occur in conventional supersymmetric quantum mechanics with real potential. An explicit example of a non-trivial set of isospectral potential is also obtained. © 2002 Elsevier Science B.V. All rights reserved.

Isospectral partners of a complex PT-invariant potential

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified nonpolynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.

Modern Physics Letters A

PT-symmetric nonpolynomial oscillators and hyperbolic potential with two known real eigenvalues in a susy framework

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT nonsymmetric and its known eigenvalue corresponds to an unbound state.

Generating complex potentials with real eigenvalues in supersymmetric quantum mechanics

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.

sl(2,C) as a complex lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues

A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian. The formalism admits vanishing Witten index. (C) 2000 Elsevier Science B.V.

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Supersymmetry without hermiticity within PT symmetric quantum mechanics

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	International Journal of Modern Physics A
Publisher	WORLD SCIENTIFIC PUBL CO PTE LTD
ISSN	0217-751X
Open Access	Yes