Finding the Energy Spectrum of the Quantum Hindered Rotor by the Lanczos Method
Abstract
In this thesis, the phenomenon of tunnel splitting in quantum hindered rotors is examined in detail. The mathematical basis for Lanczos methods, a family of algorithms efficient for finding extremal eigenvalues in a sparse Hermitian matrix, is investigated. An implementation of the block Lanczos method with total orthogonalization in FORTRAN 77 is upgraded and redesigned in modern FORTRAN 95. Benchmarking against analytical solutions and literature values suggest that the code is robust and the computational results show quantitative tunnel splitting results that match the qualitative predictions from quantum theory.
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