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  • 1
    Electronic Resource
    Electronic Resource
    Moment problem formulation of the simplified ideal magnetohydrodynamics ballooning equation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 717-720 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A fundamentally new method for determining the eigenvalues of linear differential operators is presented. The method involves the application of moment analysis and affords a fast and precise numerical algorithm for eigenvalue computation, particularly in the intermediate and strong coupling regimes. The most remarkable feature of this approach is that it provides exponentially converging lower and upper bounds to the eigenvalues. The effectiveness of this method is demonstrated by applying it to an important magnetohydrodynamics problem recently studied by Paris, Auby, and Dagazian [J. Math. Phys. 27, 2188 (1986)]. Through the very precise lower and upper bounds obtained, this approach gives full support to their analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528012
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  • 2
    Electronic Resource
    Electronic Resource
    A solution to the one-dimensional missing moment problem (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 32-35 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The one-dimensional "missing moment problem'' is solved using Padé analysis. The realization of this affords the most efficient framework within which to apply a Hankel–Hadamard analysis for generating rapidly convergent bounds to quantum eigenvalues. The method is applied to the quartic potential problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528185
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  • 3
    Electronic Resource
    Electronic Resource
    Variational formulation of a moment problem quantization method (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 1182-1196 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The eigenvalue moment method (EMM) has proven to be an effective technique for generating converging lower and upper bounds to the bosonic ground state energy of singular, strongly coupled, quantum systems. Application of EMM theory requires an appropriate linearization of the highly nonlinear Hankel–Hadamard (HH) moment determinant constraints for the (n+1)×(n+1) Hankel matrices Mn[u]≡Mˆn0+∑i=1msMˆniu i), dependent on the missing moment variables {u(i)}≡u. We propose an alternate variational formulation utilizing the functions Det(Mn+1[u])/Det(Mn[u]), which we prove to be locally convex over the missing moment subset satisfying the HH positivity conditions Det(Mν[u])(approximately-greater-than)0, for ν≤n. Additional features of this variational formulation facilitate its application to important problems such as the octic, sextic, and quartic anharmonic oscillators. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531455
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  • 4
    Electronic Resource
    Electronic Resource
    Moment problem formulation of the Schrödinger equation (1992)
    Springer
    Numerical algorithms 3 (1992), S. 1-16 
    Details
    ISSN: 1572-9265
    Keywords: Moment problem ; Schrödinger equation ; inequalities ; convexity ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that it is possible to project out in an exact manner the lowest eigenstate of Schrödinger equations. Taking into account the nodeless property of the lowest eigenstate one can replace the full Schrödinger equation by a moment problem whose measure is the eigenstate itself. The infinite set of positivity inequalities linked to this moment problem provides a framework which allows to compute sequences of upper and lower bounds to the unknown eigenvalue and eigenfunction. The effective computation is based on deep convexity properties embedded in the set of hierarchical inequalities associated to this moment problem. The convexity allows to get the bounds through linear programming. We illustrate the method with simple one dimensional problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02141911
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  • 5
    Electronic Resource
    Electronic Resource
    An exact projection method for the lowest eigenstate of singular multidimensional Schrödinger equations (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 32 (1987), S. 755-755 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560320777
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  • 6
    Electronic Resource
    Electronic Resource
    Systematic construction of upper and lower bounds to the ground state energy of the Schrödinger equation (1986)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 21-32 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For the multidimensional Schrödinger equation, we develop a technique based on the moment problem formulation of this equation. The method provides systematic and rapidly converging upper and lower bounds to the ground state energy, and it enjoys the following features: 1The bounds are insensitive to the strength of the perturbation; that is, the method applies even to the most singular perturbation.2The method does not require the potential to be semibounded. It applies directly to potentials whose spectrum extends from minus to plus infinity, as is the case for the Zeeman effect in hydrogenic atoms.3The presence of continuum spectrum does not affect the method: no information coming from the continuum is needed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560300705
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