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Mathematical physics

 Subject
Subject Source: Library Of Congress Subject Headings

Found in 8 Collections and/or Records:

A comparison of the upper bound to the lower bound of the doubly ionized carbon ion, 1972

 Item — Call number MU Thesis Gue
Identifier: b2088518
Abstract

The objective of this thesis is to compare the upper bound of the ground state energy of doubly ionized carbon (C⁺⁺) to the lower bound obtained by reduced density matrices.

To make a fair comparison, the number of orbitals used in both is the same, namely ten. The upper bound is obtained by use of the standard Rayleigh-Ritz Variational Principle which states ⟨Ψ|H|Ψ⟩ ≥ Eo(H) were Eo(H) is the exact ground state energy, H is the Hamiltonian, and Ψ is the trial wave function.

Dates: 1972

An improved ground state wavefunction for helium for use in density matrix calculations, 1972

 Item — Call number MU Thesis Bar
Identifier: b2088644
Abstract An improved ground state wavefunction for Helium for use in density matrix calculations has been obtained. This improvement was achieved by the introduction into the expansion for the singlet S-state wavefunction for Helium, of a term containing explicit angular dependence. This angular term was constructed so as to preserve angular momentum symmetry by being an eigenfunction of the two-particle, angular momentum operator with eigenvalue zero, as is required for S-states. The results give...
Dates: 1972

Application of perturbation theory to one-electron systems, 1971

 Item — Call number MU Thesis Tru
Identifier: b2088584
Abstract The solution to the problem of a one-electron ion under the influence of various generalized central-field potentials is considered. Solutions are obtained using a finite expansion of the perturbation wave functions in terms of associated Laguerre polynomials. Higher orders of perturbation theory are obtained without having to perform integrations over the continuum states, and the solution can be written explicitly to any order. This perturbation procedure is applied to the three...
Dates: 1971

Approximate methods in quantum mechanics, 1969

 Item — Call number MU Thesis LaF
Identifier: b2088192
Abstract A survey of the relative efficiency of various approximate methods for solving the non-relativistic Schroedinger Equation [sic] is made. In particular, a comparison is made of the results obtained for the problem of a simple harmonic oscillator perturbed by λx∝, (∝ =3,4 ) while using the Rayleigh-Ritz variational principle, Linear Variation of Functions, and the Reyleigh-Schroedinger [sic]...
Dates: 1969

Calculation of lower bounds to the ground state energy of the C⁺⁺ ion utilizing the technique of reduced density matrices subject to continuously variable N-representability constraints, 1974

 Item — Call number MU Thesis Gor
Identifier: b2088648
Abstract

A recently developed theory enabling the construction of density matrices which are expressible in terms of a given spin geminal set and which are a nearly N-representable as possible is discussed.

Calculation of lower bounds to the ground state energy of the C⁺⁺ ion is performed utilizing reduced density matrices subject to the continuously variable N-representability constraint determined by the above mentioned theory.

Dates: 1974

Density matrix techniques, 1970

 Item — Call number MU Thesis Tra
Identifier: b2088112
Abstract The objective of this paper is to demonstrate the usefulness of density matrix techniques in the determination of the ground state energy of certain atomic systems. Use of the method, currently under development, results in a lower energy bound in contrast with the Rayleigh-Ritz method which yields an upper bound. The former technique is illustrated for the C⁺⁺ atomic system. It was found that the Pauli Principle was being violated even when the 2-particle density matrix is expanded in...
Dates: 1970

High order perturbation theory and the harmonic oscillator, 1970

 Item — Call number MU Thesis Osc
Identifier: b2088115
Abstract In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form λx∝ are studied were λ is the coupling constant. The method is demonstrated by a general derviation of the wavefunctions to third order for any ∝ and quantum number n. Additonal expressions are presented for the ground states to tenth order in the energy. It is also shown that the "matching condition" for the basic and...
Dates: 1970

Two electron system calculations applied to reduced density matrices, 1970

 Item — Call number MU Thesis Pra
Identifier: b2088114
Abstract The non-relativistic energies have been determined for the singlet and triple S states (1¹S, 2¹S and 2³S) of the helium like two electron system. Calculations were based on a finite set of orbitals of the order 7. The set, which includes Laguerre polynomials, is expressed as a superposition of configurations built up from one-electron wave functions or orbitals and approximates the exact wave function. Application of the variational principle leads to a system of linear equations....
Dates: 1970