Journal
PHYSICS OF ATOMIC NUCLEI
Volume 75, Issue 1, Pages 109-117Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S1063778811070192
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Recent developments associated with old technique of generating functions and invariant theory which I have started to apply to molecular problems due to my collaboration with Yu.F. Smirnov about 25 years ago are discussed. Three aspects are presented: the construction of diagonal in polyad quantum number effective resonant vibrational Hamiltonians using the symmetrized Hadamard product; the decomposition of the number of state generating function into regular and oscillatory contributions and its relation with Todd polynomials and topological characterization of energy bands; qualitative aspects of resonant oscillators and fractional monodromy as one of new generalizations of Hamiltonian monodromy.
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