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Lagrange Meshes in Hardronic Physics

Title: Lagrange Meshes in Hardronic Physics.
Name(s): Bryant, Brandon, author
Type of Resource: text
Genre: Text
Issuance: serial
Date Issued: 2011
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: In hadronic physics, the potentials of hadrons are not known and, therefore, their wave functions are not known either. The wave functions can be used to calculate energy spectra and other properties of hadrons, like decay rates. Some hadronic physicists resort to approximation methods to describe the wave functions. In this project, we express wave functions as expansions of basis functions that contain orthogonal polynomials and then employ them in a variational method. We apply this technique to 2 different systems with known wave functions for 2 different bases. We find that with an appropriately chosen basis of sufficient size this technique produces accurate wave functions and energy spectra. Choosing a sufficiently large basis becomes problematic in practice because of the computational time required to perform eigenvalue calculations. It is desirable then to employ an efficient means of computation. We address this issue by use of the Lagrange mesh method. This method is an approximate variational calculation that gives a potential matrix which is diagonal and a kinetic matrix that must only be calculated once for a given basis. Furthermore, each nonzero element in the potential matrix requires evaluation at only 1 mesh point and each element in the kinetic matrix requires evaluation at only 1 or 2 mesh points. We apply the Lagrange mesh method to a problem with an exact, known solution and then to a hadronic problem. We find that this method is easily implemented and gives accurate results.
Identifier: FSU_migr_uhm-0006 (IID)
Keywords: Lagrange mesh, Hadron, Hamiltonian
Submitted Note: A Thesis submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Honors in the Major.
Degree Awarded: Spring Semester, 2011.
Date of Defense: April 19, 2011.
Subject(s): Physics
Persistent Link to This Record:
Restrictions on Access:
Owner Institution: FSU
Is Part of Series: Honors Theses.

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Bryant, B. (2011). Lagrange Meshes in Hardronic Physics. Retrieved from