{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-2184"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-2184","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well","abstract":"The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr\\\"{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\\psi(x)$. The system naturally imposes an additional condition at $\\psi(0)$ due to the Dirac delta function, which yields the final equation for the energy levels $\\{E_n\\},$ that has infinitely many solutions. In the second part, a lattice potential within the infinite well is considered, which is defined as a finite sum of Dirac delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis should be done on these systems, as well as expanding the problem to several dimensions.","abstract_html":"The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr\\&quot;{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\\psi(x)$. The system naturally imposes an additional condition at $\\psi(0)$ due to the Dirac delta function, which yields the final equation for the energy levels <span class=\"etd-inline-math\">\\{E<sub>n</sub>\\},</span> that has infinitely many solutions. In the second part, a lattice potential within the infinite well is considered, which is defined as a finite sum of Dirac delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis should be done on these systems, as well as expanding the problem to several dimensions.","abstract_has_math":true,"creators":["Craig, Samantha M"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Belinskiy, Boris","Cox, Christopher L.; Kong, Lingju; Nichols, Roger","College of Arts and Sciences"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:47:21Z","subjects":["Differential equations","Dirac equation","Quantum theory","Schrödinger equation"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/1000","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Belinskiy, Boris","Cox, Christopher L.; Kong, Lingju; Nichols, Roger","College of Arts and Sciences"]},{"key":"dc:creator","label":"Author","values":["Craig, Samantha M"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-05-01T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Differential equations","Dirac equation","Quantum theory","Schrödinger equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/1000"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr\\\"{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\\psi(x)$. The system naturally imposes an additional condition at $\\psi(0)$ due to the Dirac delta function, which yields the final equation for the energy levels $\\{E_n\\},$ that has infinitely many solutions. In the second part, a lattice potential within the infinite well is considered, which is defined as a finite sum of Dirac delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis should be done on these systems, as well as expanding the problem to several dimensions."]},{"key":"dc:title","label":"Title","values":["The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well"]}]}],"canonical_facts":{"dc:contributor":["Belinskiy, Boris","Cox, Christopher L.; Kong, Lingju; Nichols, Roger","College of Arts and Sciences"],"dc:creator":["Craig, Samantha M"],"dc:date":["2025-05-01T07:00:00Z"],"dc:description":["Dept. of Mathematics","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."],"dc:description.abstract":["The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr\\\"{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\\psi(x)$. The system naturally imposes an additional condition at $\\psi(0)$ due to the Dirac delta function, which yields the final equation for the energy levels $\\{E_n\\},$ that has infinitely many solutions. In the second part, a lattice potential within the infinite well is considered, which is defined as a finite sum of Dirac delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis should be done on these systems, as well as expanding the problem to several dimensions."],"dc:identifier":["https://scholar.utc.edu/theses/1000"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Differential equations","Dirac equation","Quantum theory","Schrödinger equation"],"dc:title":["The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:47:21Z"}