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.

B BAGCHI

C QUESNE

M ZNOJIL

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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

Modern Physics Letters A

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

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 examine a generalized PT-symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity ε. We make use of the Bender-Dunne operator basis elements and exploit the properties of the totally symmetric operator Tm,n. © World Scientific Publishing Company.

A perturbative treatment of a generalized PT-symmetric quartic anharmonic oscillator

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 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.

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

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

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	Modern Physics Letters A
Publisher	WORLD SCIENTIFIC PUBL CO PTE LTD
ISSN	0217-7323
Open Access	Yes