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.

B BAGCHI

S MALLIK

H BÃ­LA

V JAKUBSKÃ½

M ZNOJIL

C QUESNE

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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

International Journal of Modern Physics A

PT-symmetric supersymmetry in a solvable short-range model

We show that complex Lie algebras (in particular s1(2, ℂ)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: Complexified Scarf II, generalized Pöschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudo-Hermiticity are also discussed. © 2002 Elsevier Science B.V. All rights reserved.

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

Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength Z lies below the critical value Z 0 (c) where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of sec 2-like potentials in the Z → 0 limit. For Z above Z 0 (c), there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.

Modern Physics Letters A

PT-symmetric square well and the associated SUSY hierarchies

The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples.

Generalized continuity equation and modified normalization in PT-symmetric quantum mechanics

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.

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