The strength of the Pauli restriction on Be⁺, 1971

Item — Call Number: MU Thesis Lon

Identifier: b2089697

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: 1971

Creator

Lonnie, James M. (James Matthew) (Author, Person)
Kijewski, Louis J. (Louis Joseph) (1936-2018) (Thesis advisor, Person)
National Science Foundation (U.S.) (Funder, Organization)

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) : 43 pages ; 8.5 x 11.0 inches (28 cm).

Language of Materials

English

Additional Description

Abstract

The Schrodinger equation for an atomic system which possesses N electrons has 3N independent variables and is perhaps one of the most difficult questions in physics to solve. Because of the complex nature of the problem, only approximate methods can be used. One such method is the Rayleigh-Ritz Variational principle [sic] which minmizes over all [sic] space, and the minimum is the ground state energy. Another method is by means of density matrices. When a density matrix is assumed it is possible to impose several symmetry conditions on the density matrix. These conditions take into account the spin of the system under consideration and the orbital angular momentum. After all these symmetry conditions are taken into account, it is possible to find the one-particle density matrix and see if it satisfies the Pauli restriction. For a paticular trial two-particle density matrix with the first 14 states of helium as a basis, it is shown that the resulting one-matrix for Be⁺ does not satisfy the Pauli restriction.

Partial Contents

1. Conditions of the Gamma-Two matrix -- 2. Commutator Condition on the Gamma-Two matrix -- 3. The L_z Condition on the Gamma-Two matrix -- 4. The S_z Condition on the Gamma-Two matrix -- 5. The M_± Condition on the Gamma-Two matrix -- 6. The L₊ Condition on the Gamma-Two matrix -- 7. The S₊ Condition on the Gamma-Two matrix -- 8. The tr r⁽²⁾ Condition -- 9. The tr (S(X₁) + S(X₂))² r⁽²⁾ Condition -- 10. The tr (S_z(X₁) + S_z(X₂))² r⁽²⁾ Condition -- 11. The Bopp Condition -- 12. The Gamma-One matrix -- 13. The Gamma-One matrix for the 1¹S and 2¹S states -- 14. The Gamma-One matrix for the 2³S states -- 15. The Gamma-One matrix for the 2³P states -- 16. The Gamma-One Ensemble matrix.