Two electron system calculations applied to reduced density matrices, 1970

Item — Call Number: MU Thesis Pra

Identifier: b2088114

Staff Only

Scope and Contents

From the Collection:

The collection consists of theses written by students enrolled in the Monmouth College graduate Physics program. The holdings are bound print documents that were submitted in partial fulfillment of requirements for the Master of Science degree.

Dates

Creation: 1970

Creator

Pratt, Isaac H. (Isaac Harold) (1920-1984) (Author, Person)
Kijewski, Louis J. (Louis Joseph) (1936-2018) (Thesis advisor, Person)
Tranchina, John P. (Data contributor, Person)

Conditions Governing Access

The collection is open for research use. Access is by appointment only.

Access to the collection is confined to the Monmouth University Library and is subject to patron policies approved by the Monmouth University Library.

Collection holdings may not be borrowed through interlibrary loan.

Research appointments are scheduled by the Monmouth University Library Archives Collections Manager (723-923-4526). A minimum of three days advance notice is required to arrange a research appointment for access to the collection.

Patrons must complete a Researcher Registration Form and provide appropriate identification to gain access to the collection holdings. Copies of these documents will be kept on file at the Monmouth University Library.

Extent

1 Items (print book) : 100 pages ; 8.5 x 11.0 inches (28 cm).

Language of Materials

English

Additional Description

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. The condition for solubility is given by the secular equation which determines the eigenvalues. The values of the coefficients in the expansion of the wave function are determined by diagonalizing the resulting matrix by the Jacobi method.

Reduced one particle density matrices were obtained in terms of the finite set of Laguerre functions. These matrices were then used to construct a trial density matrix for a higher order ion (C⁺⁺) so as to determine the possibility of satisfying the Pauli principle.

Partial Contents

Abstract -- 1. Introduction -- 2. Solution of the Schrodinger function -- 3. Method of linear variation function -- 4. Radial function - Laguerre polynomial -- 5. Calculations (singlet) -- 6. Calculations (triplet) -- 7. Density matrices -- 8. Applications of density matrices to C⁺⁺ -- 9. Results -- 10. Conclusions -- Acknowlegement -- References -- Appendices.