Problems in Quantum Mechanics

Constantinescu, Florin; Magyari, E.; Wilson, Timothy M.

doi:10.1119/1.1986548

Cited by 52 publications

(75 citation statements)

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“…[31]). One should notice that this model works with the differential pseudo-Hermitian operator with structure which strongly resembles the usual Schrödinger operators in the simplest non-trivial, twodimensional coupled-channel case.…”

Section: Discussionmentioning

confidence: 99%

${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$

Bagchi

Banerjee

Caliceti

et al. 2005

Int. J. Mod. Phys. A

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A brief overview is given of recent developments and fresh ideas at the intersection of PT − and/or CPT −symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of CPT −symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of CPT −symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be PT −asymmetric.

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Section: Discussionmentioning

confidence: 99%

${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$

Bagchi

Banerjee

Caliceti

et al. 2005

Int. J. Mod. Phys. A

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“…Though this explicit representation can be used for our problem [24,25], it is not really necessary since all our results are representation independent. The relativistic recurrence relation we are after, can be deduced using a similar reasoning as the used in section II for the non-relativistic case.…”

Section: The Relativistic Recurrence Relationsmentioning

confidence: 99%

“…Equations (23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33) are the basic equations of our problem. To proceed, we consider, as in the non-relativistic case, radial functions of the form f (r) = r λ and insert the explicit expression for the Coulomb potential: V (r) = −Z/r.…”

Section: The Relativistic Recurrence Relationsmentioning

confidence: 99%

Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements

Martínez‐y‐Romero

Núñez‐Yépez

Salas‐Brito

2001

J. Phys. B: At. Mol. Opt. Phys.

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Abstract.General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schrödinger case. A relativistic version of the PasternackSternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form r λ and βr λ -where β is a Dirac matrix-are presented.

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“…The low popularity of the conceptual as well as practical use of the bound-state families as described by Eqs. (1) and (2) may be given several tentative explanations. We shall return to this point later, in section 4 below.…”

Section: Introductionmentioning

confidence: 99%

Symmetrized exponential oscillator

Znojil

2016

Mod. Phys. Lett. A

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Several properties of bound states in potential V (x) = g 2 exp(|x|) are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz., asymptotically decreasing or regular) exact Bessel-function forms which obey the asymptotic or matching conditions, respectively. The merits of the resulting complementary transcendental secular equation approaches are compared and their applicability is discussed.

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Problems in Quantum Mechanics

Cited by 52 publications

References 0 publications

${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$

${\mathcal{CPT}}$-CONSERVING HAMILTONIANS AND THEIR NONLINEAR SUPERSYMMETRIZATION USING DIFFERENTIAL CHARGE-OPERATORS ${\mathcal C}$

Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements

Symmetrized exponential oscillator

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