Adina Ceausu-Velcescu

Some further considerations on deriving matrix elements of non-periodic potentials in the basis of the non-degenerate harmonic oscillator wavefunctions

Abstract Using the properties of the generating function of the Hermite polynomials, we have calculated the matrix elements for the Gaussian-type potential V G (x)=A exp {−B(x−C) 2 } and for the Morse-type potential VM(x)=De[1−exp(−ax)]2 in the basis of the non-degenerate harmonic oscillator wavefunctions. The final forms of these matrix elements are very simple to use and hence suitable for the numerical resolution of the Schrodinger equation for multiple-well potentials or anharmonic oscillators.

The ν6 = 1 state of fluoroform, HCF3: analysis of the rotational and vibrational spectra

Abstract An analysis of the ν 6 =1 state of fluoroform is performed using rotational and high resolution infrared spectra. Previously radiofrequency data [Chem. Phys. Lett. 214 (1993) 265–270] and millimeter data [J. Mol. Spectrosc. 131 (1988) 1–8] were combined with new millimeter and infrared measurements, and a set of 27 parameters has been derived. A multiple fit analysis was performed confirming the assumption that the ν 6 =1 excited state is not affected by intervibrational resonances.

Frequency-comb-assisted precision laser spectroscopy of CHF3 around 8.6 μm

We report a high-precision spectroscopic study of room-temperature trifluoromethane around 8.6 μm, using a CW quantum cascade laser phase-locked to a mid-infrared optical frequency comb. This latter is generated by a nonlinear down-conversion process starting from a dual-branch Er:fiber laser and is stabilized against a GPS-disciplined rubidium clock. By tuning the comb repetition frequency, several transitions falling in the υ5 vibrational band are recorded with a frequency resolution of 20 kHz. Due to the very dense spectra, a special multiple-line fitting code, involving a Voigt profile, is developed for data analysis. The combination of the adopted experimental approach and survey procedure leads to fractional accuracy levels in the determination of line center frequencies, down to 2 × 10(-10). Line intensity factors, pressure broadening, and shifting parameters are also provided.

Phase-space description of a particle in a quartic double-well potential

The stationary Wigner functions (WFs) have been calculated for particles evolving in a quartic double-well potential V(x) = ax2/2+bx4/4(a 0), at temperature T. In the high temperature limit, the results totally agree with those obtained using Wigners perturbative method of deriving quantum corrections to the classical distribution function. Comparison with the perturbative approach allows one to establish the range of applicability of the latter. For illustration, the second moments of the position and momentum have been calculated for the double-well potential. Furthermore, the time-evolution of the WFs for a state initially located at one of the wells has been also investigated to show the tunneling effect.