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Relativistic Treatment of Confined Hydrogen Atoms via Numerical Approximations

Noon, Jacob
http://rave.ohiolink.edu/etdc/view?acc_num=toledo152537571683933

Abstract Details

2018, Master of Science, University of Toledo, Mathematics.
The study of particles and atoms confined to spherically symmetric regions have been used to illustrate the differences between classical and quantum systems since Erwin Schrodinger's famous equation was published in 1926. Paul Dirac later added his own equation, the Dirac Equation (1928), which integrated the quantum principles that had been developing in the decades prior to Schrodinger's equation with the principles of Einstein's Special Theory of Relativity. The literature on Hydrogen atoms confined to spherically symmetric regions (using the Schrodinger equation) is abundant, with consensus on the results. To the best of our knowledge, no relativistic treatment of this problem exists (i.e., using the Dirac equation). Some reasons for this are the complexity of the Dirac equation, its solutions, and problems that arise when trying to satisfy the boundary conditions. In this paper, I will present solutions to the given problem, as well as limitations that are mathematical and physical in nature. The methods used to obtain solutions involve solving systems of first order linear ordinary differential equations analytically, and computing the roots of ratios of Kummer functions via two different numerical methods.
Ivie Stein (Committee Chair)
Robert Deck (Committee Member)
Geoffrey Martin (Committee Member)
34 p.
Applied Mathematics
Mathematical Physics; Relativistic Quantum Mechanics; Hydrogen Atom; Dirac Equation

Recommended Citations

Citations

  • Noon, J. (2018). Relativistic Treatment of Confined Hydrogen Atoms via Numerical Approximations [Master's thesis, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo152537571683933

    APA Style (7th edition)

  • Noon, Jacob. Relativistic Treatment of Confined Hydrogen Atoms via Numerical Approximations. 2018. University of Toledo, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo152537571683933.

    MLA Style (8th edition)

  • Noon, Jacob. "Relativistic Treatment of Confined Hydrogen Atoms via Numerical Approximations." Master's thesis, University of Toledo, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo152537571683933

    Chicago Manual of Style (17th edition)

toledo152537571683933
447
© 2018, some rights reserved.Creative Commons License Relativistic Treatment of Confined Hydrogen Atoms via Numerical Approximations by Jacob Noon is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Toledo and OhioLINK.