Ammonia Inversion Energy Levels using Operator Algebra
Abstract
The inversion potential for the ammonia molecule is approximated by a quartic function. The Hamiltonian thereby contains only even powers of p and x and a representation in terms of ladder operators a and a^+ is suggested. The frequency variable omega occurring in the operators is introduced as a free parameter, with its value to be determined such as to optimize agreement with experimental results. Using known structural parameters of the ammonia molecule, the eigenvalues for a 10 by 10 truncation of the Hamiltonian matrix are computed. The splitting between the two lowest eigenvalues corresponds to the ammonia maser frequency, 24.87 GHz, this value being reproduced by the appropriate choice of omega.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.08178
 Bibcode:
 2018arXiv180908178B
 Keywords:

 Physics  Chemical Physics
 EPrint:
 5 pages, 4 figures