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.

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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 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.

Modern Physics Letters A

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

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

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

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.

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

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.

International Journal of Modern Physics A

Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues

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	Data powered by TypesetPhysics Letters, Section A: General, Atomic and Solid State Physics
Publisher	Data powered by TypesetELSEVIER SCIENCE BV
ISSN	0375-9601
Open Access	Yes