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Pointwise Reconstruction of Wave Functions from Their Moments through Weighted Polynomial Expansions: An Alternative Global-Local Quantization Procedure. MATHEMATICS 2015. [DOI: 10.3390/math3041045] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Dhatt S, Bhattacharyya K. Asymptotic response of observables from divergent weak-coupling expansions: a fractional-calculus-assisted Padé technique. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:026711. [PMID: 23005886 DOI: 10.1103/physreve.86.026711] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2012] [Indexed: 06/01/2023]
Abstract
Appropriate constructions of Padé approximants are believed to provide reasonable estimates of the asymptotic (large-coupling) amplitude and exponent of an observable, given its weak-coupling expansion to some desired order. In many instances, however, sequences of such approximants are seen to converge very poorly. We outline here a strategy that exploits the idea of fractional calculus to considerably improve the convergence behavior. Pilot calculations on the ground-state perturbative energy series of quartic, sextic, and octic anharmonic oscillators reveal clearly the worth of our endeavor.
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Affiliation(s)
- Sharmistha Dhatt
- Department of Chemistry, University of Calcutta, Kolkata, India.
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Handy CR, Khan D, Okbagabir S, Yarahmad T. Moment problem quantization within a generalized scalet-Wigner (auto-scaling) transform representation. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/6/308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Yan Z, Handy CR. Extension of a spectral bounding method to the PT-invariant states of the −(iX)Nnon-Hermitian potential. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/46/313] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Handy CR. Generating converging bounds to the (complex) discrete states of theP2+ iX3+ iαXHamiltonian. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/24/305] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Handy CR, Lee P. Positivity and the energy quantization of physical systems: the C-shift moment method. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/7/027] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Handy CR, Hayes H, Stephens DV, Joshua J, Summerour S. Application of the eigenvalue moment method to important one-dimensional quantum systems. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/26/11/013] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Handy CR, Murenzi R. Continuous wavelet transform analysis of one-dimensional quantum bound states from first principles. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:3754-3763. [PMID: 9913919 DOI: 10.1103/physreva.54.3754] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kravchenko YP, Liberman MA, Johansson B. Highly Accurate Solution for a Hydrogen Atom in a Uniform Magnetic Field. PHYSICAL REVIEW LETTERS 1996; 77:619-622. [PMID: 10062860 DOI: 10.1103/physrevlett.77.619] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Kravchenko YP, Liberman MA, Johansson B. Exact solution for a hydrogen atom in a magnetic field of arbitrary strength. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 54:287-305. [PMID: 9913479 DOI: 10.1103/physreva.54.287] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wang JH, Hsue CS. Calculation of the energy levels of a hydrogen atom in a magnetic field of arbitrary strength by using B splines. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:4508-4514. [PMID: 9912789 DOI: 10.1103/physreva.52.4508] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR. Extension of a moment-problem minimax quantization procedure to anharmonic potentials. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:3468-3473. [PMID: 9912646 DOI: 10.1103/physreva.52.3468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR, Appiah K, Bessis D. Moment-problem formulation of a minimax quantization procedure. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:988-996. [PMID: 9910985 DOI: 10.1103/physreva.50.988] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Zang JX, Rustgi ML. Energy levels of a hydrogen atom in a magnetic field. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:861-862. [PMID: 9910964 DOI: 10.1103/physreva.50.861] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chen Z, Goldman SP. Relativistic variational calculations with finite nuclear size: Application to hydrogenic atoms in strong magnetic fields. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:1107-1113. [PMID: 9909711 DOI: 10.1103/physreva.48.1107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Falsaperla P, Fonte G. Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous bound-state error estimates in the weak-field regime. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:4143-4153. [PMID: 9909420 DOI: 10.1103/physreva.47.4143] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Xi J, He X, Li B. Energy levels of the hydrogen atom in arbitrary magnetic fields obtained by using B-spline basis sets. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:5806-5811. [PMID: 9908833 DOI: 10.1103/physreva.46.5806] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR. An eigenvalue moment method analysis of the V( x) = [ω 2/2] x2+ α x3+ β x4anharmonic oscillator. Mol Phys 1992. [DOI: 10.1080/00268979200102011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Handy CR. Application of the eigenvalue moment method to the quartic anharmonic double-well oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:1663-1666. [PMID: 9908289 DOI: 10.1103/physreva.46.1663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chen Z, Goldman SP. Relativistic and nonrelativistic finite-basis-set calculations of low-lying levels of hydrogenic atoms in intense magnetic fields. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:1722-1731. [PMID: 9907156 DOI: 10.1103/physreva.45.1722] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chen Z, Goldman SP. Relativistic calculations for hydrogenic atoms in strong magnetic fields with Slater-type basis functions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:4459-4463. [PMID: 9906486 DOI: 10.1103/physreva.44.4459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Goldman SP, Chen Z. Generalized relativistic variational calculations for hydrogenic atoms in arbitrary magnetic fields. PHYSICAL REVIEW LETTERS 1991; 67:1403-1406. [PMID: 10044138 DOI: 10.1103/physrevlett.67.1403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Handy CR, Giraud BG, Bessis D. Dynamical-system formulation of the eigenvalue moment method. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:1505-1515. [PMID: 9906112 DOI: 10.1103/physreva.44.1505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Klein DJ, Schmalz TG, Garcriaaa-Bach MA, Valenti R, Zivkovic TP. Resonating-valence-bond theory for the square-planar lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:719-722. [PMID: 9996264 DOI: 10.1103/physrevb.43.719] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Janke W. Large-order perturbation theory of the Zeeman effect in hydrogen from a four-dimensional anisotropic anharmonic oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6071-6084. [PMID: 9903010 DOI: 10.1103/physreva.41.6071] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Fonte G, Falsaperla P, Schiffrer G, Stanzial D. Quadratic Zeeman effect for hydrogen: A method for rigorous bound-state error estimates. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:5807-5813. [PMID: 9902979 DOI: 10.1103/physreva.41.5807] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bhattacharyya K. Asymptotic response of observables from divergent power-series expansions. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:6124-6128. [PMID: 9901212 DOI: 10.1103/physreva.39.6124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR, Bessis D, Sigismondi G, Morley TD. Handy et al. reply. PHYSICAL REVIEW LETTERS 1989; 62:2199. [PMID: 10039883 DOI: 10.1103/physrevlett.62.2199] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Tokura Y, Fujimori A, Matsubara H, Watabe H, Takagi H, Uchida S, Sakai M, Ikeda H, Okuda S, Tanaka S. Electron and hole doping in Nd-based cuprates with single-layer CuO2 sheets: Role of doped Ce ions and 30-K superconductivity. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:9704-9707. [PMID: 9947733 DOI: 10.1103/physrevb.39.9704] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Rech PC, Gallas MR, Gallas JA. Comment on "Rapidly converging bounds for the ground-state energy of hydrogenic atoms in superstrong magnetic fields". PHYSICAL REVIEW LETTERS 1989; 62:2198. [PMID: 10039882 DOI: 10.1103/physrevlett.62.2198] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Shertzer J. Finite-element analysis of hydrogen in superstrong magnetic fields. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3833-3835. [PMID: 9901703 DOI: 10.1103/physreva.39.3833] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR, Mantica G, Gibbons JB. Quantization of lattice Schrödinger operators via the trigonometric moment problem. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3256-3259. [PMID: 9901625 DOI: 10.1103/physreva.39.3256] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR, Pei JQ. Moment-method analysis of the ground state of discretized bosonic systems. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:3175-3181. [PMID: 9900746 DOI: 10.1103/physreva.38.3175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Handy CR, Luo L, Mantica G, Msezane AZ. Exact bounds to one-dimensional potential scattering amplitudes through the classical theory of moments. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:490-493. [PMID: 9900189 DOI: 10.1103/physreva.38.490] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Handy CR, Bessis D, Morley TD. Generating quantum energy bounds by the moment method: A linear-programming approach. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:4557-4569. [PMID: 9899601 DOI: 10.1103/physreva.37.4557] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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