ALGEBRAIC MANIPULATIONS WITH COMPUTERS. RECENT PROGRESS IN THE FIELD OF MOLECULAR SPECTROSCOPY
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Publisher:Ohio State University
The great accuracy now currently obtained in experimental Molecular Spectroscopy has brought into evidence the necessity of developing the theoretical calculations up to very high orders of approximation. No need to say how dreadfully complex such calculations become. It is clear that the main difficulty lies in the fact that most of the quantities which are to be manipulated do not commute. The algebra we have defined during the past years allows a computer to perform very rapidly the literal developments of the formalism and, particularly: - any kind of canonical transformation of the vibro-rotational Hamiltonian, or the dipolar momentum of a molecule (which means: computation of the commutator of two polynomials depending on any number of non commutative sets of operators); - product of two polynomials; - computation of the matrix elements of the operators involved in the theory; - construction of Hermitian irreducible tensors of definite symmetry. The first and the second canonical transformation of the vibrorotational Hamiltonian of a linear triatomic molecule have been recently completed and the computation times obtained demonstrate more than any other consideration the great effectiveness of the method.
Author Institution: Laboratory of Molecular Spectroscopy, Czechoslovak Academy of Sciences; Laboratoire de Spectroscopie Moleculaire, Universite de Paris
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