We solve a time-independent perturbation problem with two new numerical approximation methods and compare their results. The methods are to approximate the bound state energies of a given Hamiltonain. We also use two ”gold-standard” methods to find the bound state energies of the Hamiltonian, being the Fredholm determinant and LAPACK. These will serve as a reference point for the two new approximation methods we will test. The new methods are divergent power series in λ and their stability and speed are tested for various values of the series order N. We found that a continued fractions method with quadruple-precision is the most stable in finding the bound state energies.
|Commitee:||Gu, Jiyeong, Jaikumar, Prashanth|
|School:||California State University, Long Beach|
|Department:||Physics and Astronomy|
|School Location:||United States -- California|
|Source:||MAI 58/02M(E), Masters Abstracts International|
|Subjects:||Computational physics, Quantum physics, Physics, Particle physics|
|Keywords:||Computational, Fortran, Matrix, Particle, Physics, Quantum|
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