The adiabatic approlrbnation is applied to determine the quantum states of coupled oscillators described by ageneralized H&on-Heiles hamiltonian. Comparison with exact quantum and other results show that numerically calculated adiabatic energy levels are accurate even for excited states.
The adiabatic approximation
β Scribed by Nicholas C. Handy; Aaron M. Lee
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 384 KB
- Volume
- 252
- Category
- Article
- ISSN
- 0009-2614
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β¦ Synopsis
Now that ab initio quantum chemistry is capable of calculating vibrational frequencies ' to an accuracy of a few cm-1 ,, it becomes interesting to examine the magnitude of small contributions. We examine the magnitude of the diagonal Born-Oppenheimer correction on the bondlengths and frequencies of diatomic molecules. We also confirm that it is important to use appropriate atomic masses, rather than nuclear masses.
π SIMILAR VOLUMES
The deformation of the deuteron in the presence of a target nucleus is studied in the adiabatic approximation. Its effect on the deuteron optical potential is discussed. The contribution of deuteron break-up to this potential is also calculated.
We present an elementary proof that the quantum adiabatic approximation is correct up to exponentially small errors for Hamiltonians that depend analytically on the time variable. Our proof uses optimal truncation of a straightforward asymptotic expansion. We estimate the terms of the expansion with
Two different adiabstic methods are applied to the czkufrttion ofener~!\* IevcIs for n t~~.o-dimensional s~stcm modefin~ 3n anIwmonic S-H stretch and an associated lsarmoriic bend coupled through centrifugai stretching The two methods are compared in their ability to yield wxurate eigenvnlues for t