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Transformation for the Effective Hamiltonian

Contact Transformation for the Effective Hamiltonian.—The vibration-rotation hamiltonian of a polyatomic molecule, expressed in terms of normal co-ordinates, has been discussed in particular by Wilson, Decius, and Cross,24 and by Watson.27- 28 It is given by the following expression for a non-linearf polyatomic molecule, to be compared with equation (17) for a diatomic molecule  [Pg.132]

In these equations, Ia = lieJ is the equilibrium moment of inertia about the a principal axis, and 4° ) = The scaling factor yr is given by [Pg.133]

Vt = 2-cojr/h. Finally, returning to equation (54), Ja and ja are the components of the total angular momentum and the vibrational angular momentum about the a axis, respectively, Ja being given by [Pg.133]

The perturbation calculation may also be described as a contact transformation. The original hamiltonian is transformed to a new effective hamiltonian which has the same eigenvalues but different eigenfunctions, to some carefully chosen order of magnitude. This contact transformation of the vibration-rotation hamiltonian was originally studied by Nielsen and co-workers. 33 [Pg.134]

In more physical language, the effective rotational hamiltonian in each vibrational state is obtained by averaging the original hamiltonian over the vibrational co-ordinates using the true vibrational wavefunctions, obtained by an appropriate perturbation of the harmonic oscillator basis functions. It is an extension of the Bom-Oppenheimer separation of the electronic from the nuclear motion, to achieve a separation of the vibrational from the rotational motion. [Pg.134]




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