{"id":{"repo_id":"u-pacific","oai_identifier":"oai:scholarlycommons.pacific.edu:uop_etds-2601"},"canonical_url":"https://search.dev.ndltd.org/etd/u-pacific/oai:scholarlycommons.pacific.edu:uop_etds-2601","repository":{"repo_id":"u-pacific","name":"University of the Pacific","base_url":"https://scholarlycommons.pacific.edu/do/oai/"},"display":{"title":"Fock's representation for molecular orbitals","abstract":"V. Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R<sub>4</sub> spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R<sub>3</sub> spherical harmonics, Y<sub>1m</sub>, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy.","abstract_html":"V. Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R&lt;sub&gt;4&lt;/sub&gt; spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R&lt;sub&gt;3&lt;/sub&gt; spherical harmonics, Y&lt;sub&gt;1m&lt;/sub&gt;, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy.","abstract_has_math":false,"creators":["Shibuya, Tai-ichi"],"institution":null,"degree_name":"Master of Science (M.S.)","degree_level":"Thesis","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Carl E. Wulfman[?]"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1965,"date_issued":"1965-01-01T08:00:00Z","date_published":"1965-01-01T08:00:00Z","updated_at":"2026-07-24T05:37:34Z","subjects":["Molecular orbitals","Physical Sciences and Mathematics","Physics"],"languages":[],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/NKC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholarlycommons.pacific.edu/uop_etds/1602","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carl E. 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Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R<sub>4</sub> spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R<sub>3</sub> spherical harmonics, Y<sub>1m</sub>, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy."]},{"key":"dc:source","label":"Dc Source","values":["51"]},{"key":"dc:title","label":"Title","values":["Fock's representation for molecular orbitals"]}]}],"canonical_facts":{"dc:contributor":["Carl E. Wulfman[?]"],"dc:creator":["Shibuya, Tai-ichi"],"dc:date.available":["2018-06-29T08:42:06Z"],"dc:description.abstract":["V. Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R<sub>4</sub> spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R<sub>3</sub> spherical harmonics, Y<sub>1m</sub>, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy."],"dc:identifier":["https://scholarlycommons.pacific.edu/uop_etds/1602"],"dc:rights":["http://rightsstatements.org/vocab/NKC/1.0/"],"dc:source":["51"],"dc:subject":["Molecular orbitals","Physical Sciences and Mathematics","Physics"],"dc:title":["Fock's representation for molecular orbitals"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science (M.S.)"]},"updated_at":"2026-07-24T05:37:34Z"}