The free vibration of rectangular plates

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Instability and nonexistence of global solutions to nonlinear wave equations of the form _{}=-+ℱ()

Coupling constant analyticity for the anharmonic oscillator

This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizacker equation.

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Solutions of Hartree-Fock equations for Coulomb systems

The partitioning technique for solving secular equations is briefly reviewed. It is then reformulated in terms of an operator language in order to permit a discussion of the various methods of solving the Schrodinger equation. The total space is divided into two parts by means of a self‐adjoint projection operator O. Introducing the symbolic inverse T = (1—O)/(E—H), one can show that there exists an operator Ω = O + THO, which is an indempotent eigenoperator to H and satisfies the relations HΩ = EΩ and Ω2 = Ω. This operator is not normal but has a form which directly corresponds to infinite‐order perturbation theory. Both the Brillouin‐ and Schrodinger‐type formulas may be derived by power series expansion of T, even if other forms are perhaps more natural. The concept of the reaction operator is discussed, and upper and lower bounds for the true eigenvalues are finally derived.

Studies in Perturbation Theory. IV. Solution of Eigenvalue Problem by Projection Operator Formalism

This paper gives new results that are useful in estimation of eigenvalues of Schr\"odinger's equation. Numerical applications are made for the helium atom, an anharmonic oscillator, and a radial Schr\"odinger equation.

Lower Bounds for Eigenvalues of Schrödinger's Equation

Lower Bounds for Eigenvalues with Application to the Helium Atom

: The paper gives two new procedures for determining lower bounds to eigenvalues of semi-bounded self-adjoint operators. These procedures, while phrased in the language of Hilbert space, result in useful computational methods for the estimation of eigenvalues and eigenvectors of differential operators occurring in classical and quantum mechanics. Our procedures are based on the method of intermediate problems.

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Truncations in the method of intermediate problems for lower bounds to eigenvalues

A new procedure is given for calculation of lower bounds to the eigenvalues of self‐adjoint operators. Computation of the lower bounds is reduced to the solution of linear algebraic problems.

Norman W. Bazley

Papers

Lower Bounds for Eigenvalues of Schrödinger's Equation

Lower Bounds for Eigenvalues with Application to the Helium Atom

Truncations in the method of intermediate problems for lower bounds to eigenvalues

A Procedure for Estimating Eigenvalues

Lower bounds to eigenvalues using operator decompositions of the form B*B