Abstract
One measure of how accurately an approximate wavefunction approximatesthe true wavefunction is the overlap of the two functions. In general the truewavefunction is not known so this overlap cannot be directly calculated. Wederive two methods from the t expansion of Horn and Weinstein to bound fromabove the magnitude of the overlap of an approximate wavefunction with theground state. The first method relies on the ability to divide the Hamiltonian intoa base problem and a perturbation. The second method is more general and seemsmuch more promising.
Similar content being viewed by others
REFERENCES
R. E. Christophersen (1989). Basic Principles and Techniques of Molecular Quantum Mechanics, Springer-Verlag, New York, pp. 354–358.
J. Cioslowski (1987). Physical Review Letters, 58, 83.
D. Horn and M. Weinstein (1984). Physical Review D 30, 1256.
H. Huang (2000). Journal of Chemical Physics, 113, 456.
H. Huang, Q. Xie, Z. Cao, Z. Li, Z. Yue, and L. Ming (1999). Journal of Chemical Physics, 110, 3703.
H. Huang, X. Zeng, and L. Ming (2000). Journal of Chemical Physics, 112, 5257.
M. G. Marmorino (2000). Journal of Chemical Physics, 113, 455.
W. E. Thirring (1978). Quantum Mechanics of Atoms and Molecules, A Course in Mathematical Physics, Vol. 3, Springer-Verlag, New York, Theorem 4.6.14.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marmorino, M.G. Upper Bounds to the Overlap of Approximate and Exact Wavefunctions. International Journal of Theoretical Physics 39, 2439–2445 (2000). https://doi.org/10.1023/A:1026484903592
Issue Date:
DOI: https://doi.org/10.1023/A:1026484903592