Rudolph J. Magyar

Mentor: Carlos Gonzalez

Physical and Chemical Properties Division

Quantum Chemistry

Building 221, Room 321

Mail Stop 838

Phone: 301-975-4460

Fax: 301-869-4020

Former Sigma Xi member


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Exact solutions of the excited-state spectrum from a one-dimensional model compared to results from density functional and Hubbard methods




The one-dimensional problem of two fermions trapped in a pair of delta functions can be reduced to a one-dimensional integral equation and solved to arbitrary precision numerically.  The exact bound-state spectrum is extracted and analyzed; the results for the ground-state energy are compared to the recently developed one-dimensional LDA results and the two-site Hubbard model with exact parameters.  A one-dimensional analog of TDDFT is constructed and the resulting excited-state spectrum is also compared to the exact solution.  Despite known inaccuracies of DFT in the long separation limit (stretched H2), the density functional results are generally more accurate than the Hubbard model.  This is due to the emphasis in the Hubbard model of on-site interactions.