Numerical Computation of Time Independent and Dependent Dirac Equation Using Atomically Balanced Operator and B-Spline Basis

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  • This thesis is devoted to the numerical computation of the time-independent Dirac equation (TIDE) and the time-dependent Dirac equation (TDDE) in the prolate spheroidal coordinates. Analytical and numerical techniques including Galerkin methods, Min-max principle, and Rayleigh-Ritz methods combined with atomically balanced basis are presented to solve the Dirac equation without spectral pollution. These numerical methods are used to compute the discrete spectrum of the Dirac operator in two-center Coulomb problems for molecules $\mbox{H}_2^+$ and $\mbox{Th}_2^{179+}$. High order B-spline basis functions are used to obtain accurate results. As excepted, the numerical results do not show any spurious state.

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  • Copyright © 2014 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
Date Created
  • 2014


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