Premium
Global analysis of composite particles
Author(s) -
Story Troy L.
Publication year - 1980
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560170507
Subject(s) - hamiltonian (control theory) , operator (biology) , covariant hamiltonian field theory , amplitude , vibration , good quantum number , mathematical physics , quantum , physics , hamiltonian system , classical mechanics , quantum mechanics , superintegrable hamiltonian system , mathematics , chemistry , mathematical optimization , biochemistry , repressor , transcription factor , gene
The theory of vibrations of a composite particle when vibrational amplitudes are not constrained to be small according to the Eckart conditions is developed using the methods of differential topology. A global classical Hamiltonian appropriate for this system is given, and for the case of the molecular vibration–rotation problem, it is transformed into a global quantum Hamiltonian operator. It is shown that the zeroth‐order term in the global Hamiltonian operator is identical to the Wilson–Howard Hamiltonian; higher‐order terms are shown to give successively better approximations to the large amplitude problem. Generalized Eckart conditions are derived for the global classical Hamiltonian; the quantum equivalent of these conditions along with the quantum equivalent of the Eckart conditions are given. The spectrum of the global Hamiltonian operator is discussed and it is shown that the calculation of the vibration–rotation energy states of the system reduces to the same straight‐forward procedure, the solution of a secular determinant, as was carried out for the Wilson–Howard Hamiltonian at a later time by Nielsen.