Zhong-Qi Ma

Boson-realization model for the vibrational spectra of tetrahedral molecules

An algebraic model of boson realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with Td symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-mean-square deviation 11.61 cm(-1) The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provides a five-parameter fit with a root-mean-square deviation 12.42 cm(-1).

RELATIVISTIC LEVINSON THEOREM IN TWO DIMENSIONS

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number

Correlations of spin states for icosahedral double group

{n}_{j}

q-Deformed harmonic oscillators applied to the vibrational spectrum of methane

of the bound states and the sum of the phase shifts

Levinson’s theorem for the Schrödinger equation in two dimensions

{\ensuremath{\eta}}_{j}(\ifmmode\pm\else\textpm\fi{}M)

Algebraic Description of Anharmonic Stretching Vibrations

of the scattering states with the angular momentum

Levinson's theorem for non-local interactions in two dimensions

j

Algebraic approach to vibrational spectra of tetrahedral molecules: a case study of silicon tetrafluoride

:

Overtone Spectra and Intensities of Tetrahedral Molecules in Boson-Realization Models

{\ensuremath{\eta}}_{j}(M)+{\ensuremath{\eta}}_{j}(\ensuremath{-}M)={\left({{(n}_{j}+1)\ensuremath{\pi},\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{half}\mathrm{}\mathrm{bound}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at} E=M \mathrm{and} j=3/2 or \ensuremath{-}1/2}{{(n}_{j}+1)\ensuremath{\pi},\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{half}\mathrm{}\mathrm{bound}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at} E=\ensuremath{-}M \mathrm{and} j=1/2 or \ensuremath{-}3/2}{{n}_{j}\ensuremath{\pi} ,\mathrm{the}\mathrm{}\mathrm{remaining}\mathrm{}\mathrm{cases}.}\right)

Irreducible Bases in Icosahedral Group Space

The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half-bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.