Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schrödinger equation are constructed by starting from exactly solvable potentials for which the Schrödinger equation admits an so(2,1) potential algebra. For some of them, the zero-energy wave function is shown to be normalizable and to describe a bound state. © 1997 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

By exploiting the hidden algebraic structure of the Schrödinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable potentials. We obtain, in this way, two new classes of quasi-exactly solvable systems one of which is of periodic type while the other hyperbolic.

Journal of Physics A: Mathematical and General

A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials

Using representations of sl(2,ℝ) generators which yield associated Lamé Hamiltonians we obtain new classes of elliptic potentials. We explicitly calculate eigenstates and spectra for these potentials and construct the associated orthogonal polynomials. We show that in the proper limit these potentials reduce to well-known exactly solvable potentials. © 2002 American Institute of Physics.

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